50 years ago, the mean height for women in their 20’s was 62.6 inches. Assume that...

50 years ago, the mean height for women in their 20’s was 62.6 inches. Assume that the heights of today’s women in their 20’s are approximately normally distributed with a standard deviation of 2.88 inches. If the mean height today is the same as that of a halfcentury ago, what percentage of all samples of size 25 today’s women have mean heights of at least 64.24 inches? please show work.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 62.6

standard deviation = = 2.88

n = 25

= 62.6

= / n = 2.88 / 25 = 0.576

P( >64.24 ) = 1 - P( < 64.24)

= 1 - P[( - ) / < (64.24 -62.6) /0.576 ]

= 1 - P(z <2.85 )

Using z table

= 1 - 0.9978

= 0.0022

answer= 0.22%

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In 1990, the mean height of women 20 years of age or older was 63.7 inches...

In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidence that women today are taller than in 1990? Perform the appropriate test at the 0.05 level of significance....

The height of women ages 20-29 are normally distributed, with a mean of 64.3 inches. Assume...

The height of women ages 20-29 are normally distributed, with a mean of 64.3 inches. Assume sigmaequals2.5 inches. Are you more likely to randomly select 1 woman with a height less than 66.2 inches or are you more likely to select a sample of 18 women with a mean height less than 66.2 inches? Explain. What is the probability of randomly selecting 1 woman with a height of less than 66.2 inches? _______(Round to four decimal places as needed.) What...

The height of women ages 20-29 is normally distributed, with a mean of 64.2 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 64.2 inches. Assume sigmaequals2.9 inches. Are you more likely to randomly select 1 woman with a height less than 65.3 inches or are you more likely to select a sample of 29 women with a mean height less than 65.3 inches? Explain. LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal...

The height of women ages 20-29 is normally distributed, with a mean of 64.7 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 64.7 inches. Assume sigmaσequals=2.7 inches. Are you more likely to randomly select 1 woman with a height less than 67.267.2 inches or are you more likely to select a sample of 10 women with a mean height less than 67.2 inches? Explain. LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal...

The height of women ages 20-29 is normally distributed, with a mean of 64.2 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 64.2 inches. Assume σ=2.7 inches. Are you more likely to randomly select 1 woman with a height less than 66.3 inches or are you more likely to select a sample of 14 women with a mean height less than 66.3inches? Explain.

The height of women ages 20-29 is normally distributed, with a mean of 64.4 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 64.4 inches. Assume sigma = 2.6 inches. Are you more likely to randomly select 1 woman with a height less than 65.8 inches or are you more likely to select a sample of 22 women with a mean height less than 65.8 inches? Explain. What is the probability of randomly selecting 1 woman with a height less than 65.8 inches? What is the probability of selecting a...

The height of women ages 20-29 is normally distributed, with a mean of 63.6 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 63.6 inches. Assume sigma σ equals = 2.6 inches. Are you more likely to randomly select 1 woman with a height less than 65.2 inches or are you more likely to select a sample of 18 women with a mean height less than 65.2 inches? Explain.

The height of women ages 20-29 is normally distributed, with a mean of 64.7 inches. Assume...

The height of women ages 20-29 is normally distributed, with a mean of 64.7 inches. Assume sigma equals 2.7 inches. Are you more likely to randomly select 1 woman with a height less than 66 inches or are you more likely to select a sample of 30 women with a mean height less than 66 inches? Explain. What is the probability of randomly selecting 1 woman with a height less than 66 inches? What is the probability of selecting a...

Several years ago, the mean height of women 20 years of age or older was 63.7...

Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.7 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.12 . Explain what this value represents. (c) Write a conclusion for this...

The mean height of women in the United States (ages 20-29) is 64.2 inches with a...

The mean height of women in the United States (ages 20-29) is 64.2 inches with a standard deviation of 2.9 inches. A random sample of 60 women in this age group is selected. Assume that the distribution of these heights is normally distributed. Are you more likely to randomly select 1 woman with a height more than 70 inches or are you more likely to select a random sample of 20 women with a mean height more than 70 inches?...

Subjects