Unit 9 Day 10 Binomial & Normal Model Practice

4

The probability that an employee will be late to work at a large corporation is 0.21.
Give the Binomial Probability Model for looking at 5 employees:

4

The probability that an employee will be late to work at a large corporation is 0.21.
What is the probability on a given day that in a department of 5 employees exactly 3 are late.

Use:
2nd, VARS, scroll up to binompdf( (if you want to find the probability of one result)
or
use binomcdf( (if you want to find the probability of x or fewer successes among the n trials)
Enter the values for 'trials', 'p' (probability of success) and for 'x value' (the number of successes)

Enter your answer as a decimal rounded to three places.

4

The probability that an employee will be late to work at a large corporation is 0.21.
What is the probability on a given day that in a department of 5 employees at most 3 are late.

See #2 for instructions on using the TI-84 calculator.

Enter your answer as a decimal rounded to three places.

4

The probability that an employee will be late to work at a large corporation is 0.21.
What is the probability on a given day that in a department of 5 employees at least 3 are late.
Be careful, at least three means the complement of at most 2.
Ex. P(at least three are late)=1-P(at most 2 are late)

See #2 for instructions on using the TI-84 calculator.

Enter your answer as a decimal rounded to three places.

4

The probability that an employee will be late to work at a large corporation is 0.21.
What is the probability on a given day that in a department of 5 employees 1 or 2 employees are late.

Hint: P(1 OR 2)= P(exactly 1 is late) OR P(exactly 2 are late), what does OR mean you should do...?

See #2 for instructions on using the TI-84 calculator.

Round at the END of your calculations, enter your answer as a decimal rounded to three places.

4

The probability that an employee will be late to work at a large corporation is 0.21.
A large department has 110 employees. What is the expected value of the number of employees that will be late on any given day?

Enter your answer as a decimal rounded to three places.

4

The probability that an employee will be late to work at a large corporation is 0.21.
A large department has 110 employees.
What is the standard deviation for the number of employees that will be late on any given day?

Enter your answer as a decimal rounded to three places.

3

Remember, to be statistically significant, the z-score for a value needs to be more than 2 standard deviations from the mean.

Is the following result statistically significant?
A value of 165.4 in a Normal model with a mean of 151.7 and a standard deviation of 11.6 Remember:

1. Calculate the z-score. 2. Is this statistically significant?
3. Explain why this is/is not statistically significant.

3

Is the following result statistically significant?
A value of 23.2 in a normal model of N(65, 21.2) Remember:

1. Calculate the z-score. 2. Is this statistically significant?
3. Explain why this is/is not statistically significant.

3

Is the following result statistically significant?
A weight of a 561 pound pig where the weights are modeled by N(425 lb, 63 lb) Remember:

1. Calculate the z-score. 2. Is this statistically significant?
3. Explain why this is/is not statistically significant.

4

A basketball player who ordinarily makes about 65% of his free throw shots has new sneakers, which he thinks improve his game.
Over his past 40 shots with the new sneakers he has made 31. Do you think his chances of making a shot really increased? Did his shooting increase significantly?
(you will need to do some calculations before you can check the statistical significance) p=.65 q=.35 n=40
First you need to calculate the Expected value (mean) and the standard deviation, write these down so you can use them to calculate the z-score. See #6 & #7 for the formulas.

Now: calculate the z-score. (see #10 for the formula)
Enter the z-score below rounded to three places past the decimal.

4

Is the data in #11 statistically significant?
1. Did the new sneakers significantly increase the basketball player's ability to make baskets during a game?
2. How do you know?

4

A Department of Transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers.
Suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight.
Can you consider the fate of these bags to be Bernoulli trials?
Use 2 P I N to explain why or why not.
(Remember the 10% Rule, if the sample is less than 10% of the population then we can assume trials are independent).

6

A basketball player makes 72.5% of her free throws.
What is the probability that she makes at least 35 of her next 60 shots?

We would like to use the Normal Model to estimate the probability.
Check to see if the Success/Failure condition is met by the free throws (so you can use the Normal Model).
Here are the conditions:
1. Check the value of np
2. Check the value of nq
3. How do you know if you can use the Normal Model?
Select all answers that apply.

4

A basketball player makes 72.5% of her free throws.
What is the probability that she makes at least 35 of her next 60 shots?
n=60, p=0.725, x=35
1st calculate the expected value (mean) for this situation and the standard deviation (write them down).
See #6 & #7 for the formulas.

2nd calculate the z-score. See #10 for the formula.

Enter the z-score. You will use it in the next problem.

4

A basketball player makes 72.5% of her free throws.
What is the estimated probability that she makes at least 35 of her next 60 shots?

Now: use 2nd, VARS, Normalcdf, enter your lower and upper values for the z-scores, keep the mean=0 and sigma=1
Remember when we did Normal Model calculations:
if you want the upper tail probability use 'upper: 99'
if you want the lower tail probability use 'lower: -99'

Enter the estimated probability as a decimal rounded to three places.

4

A basketball player makes 72.5% of her free throws.
What is the exact probability that she makes at least 35 of her next 60 shots?
Hint: this means you need to use Binompdf or Binomcdf
You also need to think about what 'at least 35' means you need to do. (complement of 'no more than')
1-???

Enter the probability rounded to three places past the decimal.

4

14% of smart phones require servicing in their first year.
What is the exact probability that no more than 10 smart phones in a shipment of 100 will need such repair?
Use binompdf or binomcdf.

4

14% of smart phones require servicing in their first year.
What is the estimated probability that no more than 10 smart phones in a shipment of 100 will need such repair?
The Success/Failure condition is met because np=14 and nq=86, so we can use the Normal Model.

First you will need to calculate the mean (expected value) and the standard deviation (sigma), (See #6 & #7 for the formulas).
Then find the z-score. (see #10 for the formula)
Enter the z-score below, round to three places.

4

14% of smart phones require servicing in their first year.
What is the estimated probability that no more than 10 smart phones in a shipment of 100 will need such repair?
Now that you've found the z-score, use it to find the estimated probability with the Normal Model.
Use 2nd, VARS, Normalcdf, enter the lower and upper limits.

4

6% of scratch-off lottery tickets have a prize of a free ticket.
What is the probability that this prize is on 10 of the 200 tickets at the local convenience store?
Find the exact probability.
n= 200 p=0.06
Enter your probability as a decimal rounded to three places.
Hint: you need to decide if you will use binompdf or binomcdf and how.

4

6% of scratch-off lottery tickets have a prize of a free ticket.
What is the probability that this prize is on 15 or more of the 200 tickets at the local convenience store?
(this could also be thought of as 'at least 15', which means use the complement of no more than 14)

Find the exact probability. Enter your probability as a decimal rounded to three places.
Hint: you need to decide if you will use binompdf or binomcdf and how.

The probability that an employee will be late to work at a large corporation is 0.21. Give the Binomial Probability Model for looking at 5 employees:

The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at most 3 are late.See #2 for instructions on using the TI-84 calculator.Enter your answer as a decimal rounded to three places.

The probability that an employee will be late to work at a large corporation is 0.21. A large department has 110 employees. What is the expected value of the number of employees that will be late on any given day?Enter your answer as a decimal rounded to three places.

The probability that an employee will be late to work at a large corporation is 0.21. A large department has 110 employees. What is the standard deviation for the number of employees that will be late on any given day?Enter your answer as a decimal rounded to three places.

Is the following result statistically significant?A value of 23.2 in a normal model of N(65, 21.2) Remember:1. Calculate the z-score. 2. Is this statistically significant?3. Explain why this is/is not statistically significant.

Is the following result statistically significant?A weight of a 561 pound pig where the weights are modeled by N(425 lb, 63 lb) Remember:1. Calculate the z-score. 2. Is this statistically significant?3. Explain why this is/is not statistically significant.

Is the data in #11 statistically significant? 1. Did the new sneakers significantly increase the basketball player's ability to make baskets during a game?2. How do you know?

14% of smart phones require servicing in their first year.What is the exact probability that no more than 10 smart phones in a shipment of 100 will need such repair?Use binompdf or binomcdf.

The probability that an employee will be late to work at a large corporation is 0.21.
Give the Binomial Probability Model for looking at 5 employees:

The probability that an employee will be late to work at a large corporation is 0.21.
What is the probability on a given day that in a department of 5 employees at most 3 are late.

See #2 for instructions on using the TI-84 calculator.

Enter your answer as a decimal rounded to three places.

The probability that an employee will be late to work at a large corporation is 0.21.
A large department has 110 employees. What is the expected value of the number of employees that will be late on any given day?

Enter your answer as a decimal rounded to three places.

The probability that an employee will be late to work at a large corporation is 0.21.
A large department has 110 employees.
What is the standard deviation for the number of employees that will be late on any given day?

Enter your answer as a decimal rounded to three places.

Is the following result statistically significant?
A value of 23.2 in a normal model of N(65, 21.2) Remember:

1. Calculate the z-score. 2. Is this statistically significant?
3. Explain why this is/is not statistically significant.

Is the following result statistically significant?
A weight of a 561 pound pig where the weights are modeled by N(425 lb, 63 lb) Remember:

1. Calculate the z-score. 2. Is this statistically significant?
3. Explain why this is/is not statistically significant.

Is the data in #11 statistically significant?
1. Did the new sneakers significantly increase the basketball player's ability to make baskets during a game?
2. How do you know?

14% of smart phones require servicing in their first year.
What is the exact probability that no more than 10 smart phones in a shipment of 100 will need such repair?
Use binompdf or binomcdf.