Which of the following are continuous random variables?
The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university.
Is X a discrete or a continuous random variable? Explain.
The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university.
Show that the probability distribution of X is valid.
The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university.
Compute the expected value of X. Show work on the recording document.
What does this mean? (interpret the expected value)
Which of the following is not a condition for the binomial setting?
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 two who will be entering military service?
Which is the correct set up?
In a certain large lake 30% 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 the half sheet.
Round to three places.
In a certain large lake 30% 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.
In a certain large lake 30% 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 decimal places.
Twenty 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
If the foot length of women follows a normal distribution with a mean of 23 cm, and 95% have a foot length between 17 cm and 29 cm, what is your estimate of the standard deviation of the foot lengths in this population?
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 0.372 and 0.428?
The heights of a population of men follow a normal distribution, and the middle 99.7% have heights between 60 inches and 84 inches.
What is your estimate of the mean height in this population?
Hint: sketch a normal curve or look at your flipbook.
Which of the following is the closest z-score to the 90th percentile of the standard normal distribution?
Which of the following is the closest percentile to a z-score of 1.67 in the standard normal distribution?
The proportion of pepperoni pizza orders on a randomly selected day at a local pizza shop is approximately normal with mean 0.25 and standard deviation 0.02.
Let X = the proportion of pepperoni pizza orders on a randomly selected day.
Give the notation for the normal model:
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 100 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.
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 114.5 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.
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 15.5% of Novak Djokovic’s first-serve speeds.
Round your answer to two places past the decimal.
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 3% of Novak Djokovic’s first-serve speeds.
Round your answer to two places past the decimal.
The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university.
Give the notation for “ the probability of taking at least 16 credits” in terms of X and find its probability.