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Exam 5: Normal Probability Distributions

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Question 1

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Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that He or she makes less than $28,000.

A) 0.0918
B) 0.9981
C) 0.2113
D) 0.9827

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Question 2

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SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the SAT and 25 on the ACT. Compare the scores.

A) A score of 25 on the ACT test was better.
B) A score of 1130 on the SAT test was better.
C) The two scores are statistically the same.
D) You cannot determine which score is better from the given information.

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Question 3

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Decide if it is appropriate to use the normal distribution to approximate the random variable x for a binomial experiment with sample size of n = 25 and probability of success p = 0.2

Find the area under the standard normal curve between z = 1.5 and z = 2.5.

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of babies are born Prematurely?

Find the z-score that corresponds to the given area under the standard normal curve.

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.

If the sample size is multiplied by 4, what happens to the standard deviation of the distribution of sample means?

Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } > 12 )$ to a normal probability by using the correction for continuity.

Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height between 68 And 70 inches.

In a certain normal distribution, find the mean $\mu$ when ? = 5 and 5.48% of the area lies to the left of 78.

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.

Ten percent of the population is left-handed. In a class of 100 students, write the binomial probability for the statement ?There are exactly 12 left-handed students in the class.?

Provide an appropriate response. Use the Standard Normal Table to find the probability. -An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. In one year, how many weeks would you expect the airline to lose between 10 and 20 suitcases?

Ten percent of the population is left-handed. In a class of 56 students, write the binomial probability for the statement ?There are at least 10 left-handed students in the class.?

Assume that blood pressure readings are normally distributed with $\mu$ = 120 and $\sigma$ = 8. A blood pressure reading of 145 or more may require medical attention. What percent of people have a blood pressure reading Greater than 145?

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose less than 20 suitcases?

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 120. Find the z-score corresponding to this value.

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be Less than 12.1 ounces. Find the probability if the sample is just 1 cup.

Find the z-score for which 99% of the distributionʹs area lies between -z and z.