Question

The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7 mm. Suppose that 15 individuals are randomly chosen. Round all answers to 4 where possible. What is the distribution of ¯ x ? ¯ x ~ N( , ) For the group of 15, find the probability that the average hand length is less than 186. Find the first quartile for the average adult male hand length for this sample size. For part b), is the assumption that the distribution is normal necessary? NoYes

Answer 1

Answer:

Given that:

The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7 mm. Suppose that 15 individuals are randomly chosen.

What is the distribution of ¯ x ? ¯ x ~ N( , )

The mean of the sampling distribution of sample means is.

  

The mean of the sampling distribution of sample means is 187

The standard deviation of the sampling distribution of sample means is,
  

  

The standard deviation of the sampling distribution of sample means is 1.81

For the group of 15, find the probability that the average hand length is less than 186.

For the group 15 the probability that the average hand length more than 186

First, compute the z-score then find probability based on standard normal table.

  

  

  

  

From the standard normal distribution table, the associated probability is Since find the area to the right so subtract from 1 to get

P(z > -0.55) = 1-(z < -0.55)

=1- 0.2912

= 0.7088

For the group of 15 i.e probability that the average hand length more than 186 is 0.7088

Find the first quartile for the average adult male hand length for this sample size

The first quartile is,

from. the standard normal. table the  indicated z score for the area of 0.2500 and indicative area 0.2500 is -0.67.

  

  
  

The first quartile is 185.78

Yes the assumption that the distribution is normal necessary.