Which of the following are discrete random variables?
Required
2 points
2
Question 2
2.
The probability distribution below is for the random variable X = the number of questions correct on a randomly chosen 3 question quiz.
Is X a discrete or a continuous random variable? Explain.
Required
2 points
2
Question 3
3.
The probability distribution below is for the random variable X = the number of questions correct on a randomly chosen 3 question quiz.
Show that the probability distribution of X is valid.
Required
2 points
2
Question 4
4.
The probability distribution below is for the random variable X = the number of correct questions on a randomly chosen three question quiz.
Compute the expected value of X. Show work on the recording document.
What does this mean? (Interpret the expected value)
Required
2 points
2
Question 5
5.
The probability distribution below is for the random variable X = the number of correct questions on a randomly chosen three question quiz.
Give the notation for “ the probability of getting at least 2 questions correct" in terms of X and find its probability.
Required
3 points
3
Question 6
6.
Which of the following are conditions for the binomial setting?
Required
2 points
2
Question 7
7.
Binomial Probability:
It is known that 15% of the seniors in a large high school enter military service upon graduation.
If a group of 20 seniors are randomly selected, what is the probability of observing eighteen who will be entering military service?
Which is the correct set up?
Required
2 points
2
Question 8
8.
In a certain large lake 40% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake.
Let Y = the number of fish that you throw back because they are too small.
Explain how Y can be considered a binomial random variable.
B _______
I _______
N _______
S _______
Required
2 points
2
Question 9
9.
In a certain large lake 40% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake.
Let Y = the number of fish that you throw back because they are too small.
Find the probability that exactly 5 fish are thrown back.
Show your work on your half sheet.
Round to three places.
Required
2 points
2
Question 10
10.
In a certain large lake 40% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake.
Let Y = the number of fish that you throw back because they are too small.
Calculate (5.4) and interpret the mean of Y.
Required
2 points
2
Question 11
11.
In a certain large lake 40% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake.
Let Y = the number of fish that you throw back because they are too small.
Calculate (5.4) and interpret the standard deviation of Y. Round to three places past the decimal.
Required
2 points
2
Question 12
12.
Thirty percent of all trucks undergoing a certain inspection will fail the inspection. Assume that 40 trucks are independently undergoing this inspection, one at a time.
The expected number of trucks who fail the inspection is:
Hint: expected value = mean
Required
4 points
4
Question 13
13.
The probability a person is infected by a certain cold virus is 0.3. If a random sample of 12 people is taken, what is the probability that none of the people will be infected by the cold virus? _______ Round to four places past the decimal.
What is the probability that at least one person will be infected by the cold virus? _______
Round to four places past the decimal.
Required
2 points
2
Question 14
14.
Normal Distribution: Lessons 5.5-5.7 from here on.
Estimate the mean and standard deviation of the normal density curve in the figure.
Mean = _______
Standard Deviation = _______
Required
2 points
2
Question 15
15.
If the foot length of women follows a normal distribution with a mean of 23 cm, and 95% have a foot length between 15 cm and 31 cm, what is your estimate of the standard deviation of the foot lengths in this population?
Required
2 points
2
Question 16
16.
Use the 68-95-99.7 Rule:
A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage
of observations will lie between 0.344 and 0.456?
Required
2 points
2
Question 17
17.
The heights of a population of women follow a normal distribution, and the middle 95% have heights between 58 inches and 70 inches.
What is your estimate of the mean height in this population?
Hint: sketch a normal curve or look at your flipbook.
Required
2 points
2
Question 18
18.
Which of the following is the closest z-score to the 9th percentile of the standard normal distribution?
Required
2 points
2
Question 19
19.
Which of the following is the closest percentile to a z-score of 1.02 in the standard normal distribution?
Required
2 points
2
Question 20
20.
The proportion of pepperoni pizza orders on a randomly selected day at a local pizza shop is approximately normal with mean 0.26 and standard deviation 0.03.
Let X = the proportion of pepperoni pizza orders on a randomly selected day.
Give the notation for the normal model:
Required
4 points
4
Question 21
21.
The proportion of pepperoni pizza orders on a randomly selected day at a local pizza shop is approximately normal with mean 0.26 and standard deviation 0.03.
Let X = the proportion of pepperoni pizza orders on a randomly selected day.
Use the 68–95–99.7 rule to approximate:
(a) P(X > 0.29) = _______
(b) The probability that the data values of pepperoni pizza orders is
between 0.20 and 0.35= _______
(c) The range for the middle 95% of the data values of pepperoni pizza
orders for a randomly selected day= _______ to _______
Required
3 points
3
Question 22
22.
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and standard deviation 6 mph. If you randomly choose one of Djokovic’s first serves at random, let X = its speed, measured in miles per hour.
A first serve with a speed less than 99 miles per hour is considered “slow.”
What percent of Djokovic’s first serves are slow?
Enter your answer as a decimal rounded to three places.
Required
3 points
3
Question 23
23.
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and standard deviation 6 mph. If you randomly choose one of Djokovic’s first serves at random, let X = its speed, measured in miles per hour.
A first serve with a speed more than 115.5 miles per hour is considered “fast.”
Round the z score to two places.
What percent of Djokovic’s first serves are fast?
Enter your answer as a decimal rounded to three places.
Required
3 points
3
Question 24
24.
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and standard deviation 6 mph.
Find the speed for the slowest 10.5% of Novak Djokovic’s first-serve speeds.
Keep all decimal places.
Required
0 points
0
Question 25
25.
BONUS:
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and standard deviation 6 mph. Choose one of Djokovic’s first serves at random.
Let X = its speed, measured in miles per hour.
Find the speed for the fastest 4% of Novak Djokovic’s first-serve speeds.