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Exam 7: The Normal Probability Distribution

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Question 31

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Find and Interpret the Area under a Normal Curve -more than $\$ 153,800$ if the standard deviation is $\$ 1900$ .

A) $2.5 \%$
B) $97.5 \%$
C) $47.5 \%$
D) $95 \%$

E) B) and D)
F) All of the above

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Question 32

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Find the Value of a Normal Random Variable -The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.

A) 4.7 min
B) 4.5 min
C) 4.3 min
D) 4.8 min

E) C) and D)
F) B) and D)

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Question 33

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Interpret the Area under the Standard Normal Curve as a Probability -Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { Z } < 2.25 )$ .

Find z-scores for a Given Area -Find the $z$ -score that is less than the mean and for which $70 \%$ of the distribution's area lies to its right.

Interpret the Area under the Standard Normal Curve as a Probability -Scores on a standardized test are normally distributed with a mean of 104 and a standard deviation of 20 . An individual's test score is found to be 109 . Find the $\mathrm { z }$ -score corresponding to this value.

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. - $X = 72 ; \sigma = 3$

Use Normal Probability Plots to Assess Normality -Determine whether the following normal probability plot indicates that the sample data could have come from a population that is normally distributed.

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. - $X = 68 ; \sigma = 8$

Find the Area under the Standard Normal Curve -Find the area under the standard normal curve between $\mathrm { z } = - 1.25$ and $\mathrm { z } = 1.25$ .

Approximate Binomial Probabilities Using the Normal Distribution -In a recent survey, 84% of the community favored building more parks in their neighborhood. You randomly select 18 citizens and ask each if he or she thinks the community needs more parks. Decide whether you can use the normal distribution to approximate the binomial distribution. If so, find the mean and standard deviation. If not, explain why.

Find the Value of a Normal Random Variable -The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.12 ounce. Every can that has more than 12.30 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%

Find and Interpret the Area under a Normal Curve -A firm believes the internal rate of return for its proposed investment can best be described by a normal distribution with mean 24% and standard deviation 3%. What is the probability that the internal rate of return for the investment will be at least 19.5%

Provide an appropriate response -High temperatures in a certain city for the month of August follow a uniform distribution over the interval 65°F to 87°F. What is the probability that a randomly selected August day has a high temperature that exceeded 70°F

Approximate Binomial Probabilities Using the Normal Distribution -Find the probability that in 200 tosses of a fair six-sided die, a three will be obtained at least 40 times.

Approximate Binomial Probabilities Using the Normal Distribution -Assuming that all conditions are met to approximate a binomial probability distribution with the standard normal distribution, then to compute $P ( 12 \leq x \leq 15 )$ from the binomial distribution we must compute _____as the normal approximation.

Find and Interpret the Area under a Normal Curve -Use the standard normal distribution to find $\mathrm { P } ( - 2.50 < \mathrm { z } < 1.50 )$ .

Find z-scores for a Given Area -Find the $z$ -scores for which $90 \%$ of the distribution's area lies between $- z$ and $z$ .

Use Normal Probability Plots to Assess Normality -If sample data are taken from a population that is normally distributed, a normal probability plot of the observed data values versus the expected z scores will

Find the Area under the Standard Normal Curve -Find the area under the standard normal curve to the left of $\mathrm { z } = 1.25$ .

Find the Value of a Normal Random Variable -The board of examiners that administers the real estate broker s examination in a certain state found that the mean score on the test was 451 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score Assume that the scores are normally distributed.