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Exam 5: Normal Probability Distributions

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Question 31

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The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5600. The distribution of incomes is skewed to the right. Find the mean and standard error of the mean for This sampling distribution when using random samples of size 66. Round your answers to the nearest dollar.

A) $28,520, $689
B) $28,520, $5600
C) $28,520, $66
D) $28,520, $85

E) A) and D)
F) B) and D)

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Question 32

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Find the area of the indicated region under the standard normal curve.

A) 0.1504
B) 0.1292
C) 0.8489
D) 0.0212

E) A) and B)
F) A) and C)

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Question 33

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IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

Find the probability of z occurring in the indicated region. -

Find the area under the standard normal curve between z = 1 and z = 2.

Ten percent of the population is left-handed. A class of 1800 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } \geq 15 )$ to a normal probability by using the correction for continuity.

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $29,000 and a standard deviation of $2000. What is the cutoff salary for teachers in the top 10%?

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

Use the standard normal distribution to find P(-2.25 < z < 1.25) .

The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater Than 98.4° F.

Find the probability of z occurring in the indicated region. -

Find the z-scores for which 98% of the distributionʹs area lies between -z and z.

Find the area under the standard normal curve to the left of z = 1.5.

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019.

In a certain normal distribution, find the standard deviation ? when $\mu$ = 50 and 10.56% of the area lies to the right of 55.

The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 1475 and the standard deviation was 308. The test scores of four students selected at random are 1930, 1340, 2150, and 1450. a)Find the z-scores that correspond to each value b)Determine whether any of the values are unusual.

Assume that the heights of men are normally distributed with a mean of 69.5 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 70.5 inches.

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

A recent survey found that 72% of all adults over 50 wear glasses for driving. You randomly select 33 adults over 50, and ask if he or she wears glasses. 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.