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Sampling Distributions: Mean and Standard Deviation Analysis

## Population Distribution

1.A population of values has a normal distribution with μ=70.3μ=70.3 and σ=80σ=80. You intend to draw a random sample of size n=212n=212

What is the mean of the distribution of sample means?

μ¯x=μx¯=

What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

σ¯x=σx¯=

2.A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 32 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 32 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 87 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 31.9.

P(X > 31.9) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n=87n=87 is randomly selected with a mean greater than 31.9.

P(M > 31.9) =  (Enter your answers as numbers accurate to 4 decimal places.)

3.CNNBC recently reported that the mean annual cost of auto insurance is 1019 dollars. Assume the standard deviation is 256 dollars. You take a simple random sample of 79 auto insurance policies.

Find the probability that a single randomly selected value is less than 983 dollars.

P(X < 983) =

Find the probability that a sample of size n=79n=79 is randomly selected with a mean less than 983 dollars.

P(M < 983) =

4.A population of values has a normal distribution with μ=46.6μ=46.6 and σ=88.1σ=88.1. You intend to draw a random sample of size n=210n=210.

What is the mean of the distribution of sample means?

μ¯x=μx¯=

What is the standard deviation of the distribution of sample means (i.e. the standard error)?

(Report answer accurate to 2 decimal places.)

σ¯x=σx¯=

5.A population has parameters μ=100.6μ=100.6 and σ=27.2σ=27.2. You intend to draw a random sample of size n=177n=177.

What is the mean of the distribution of sample means?

μ¯x=μx¯=

What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

σ¯x=σx¯=

6.Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 121000 dollars. Assume the standard deviation is 41000 dollars. Suppose you take a simple random sample of 79 graduates.

Find the probability that a single randomly selected policy has a mean value between 120077.4 and 133916 dollars.

P(120077.4 < X < 133916) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=79n=79 has a mean value between 120077.4 and 133916 dollars.

P(120077.4 < M < 133916) =  (Enter your answers as numbers accurate to 4 decimal places.)