Question

A random sample is drawn from a normally distributed population with mean μ = 33 and standard deviation σ = 2.1. Use Table 1. a. Are the sampling distributions of the sample mean with n = 41 and n = 82 normally distributed? Yes No b. Can you use the standard normal distribution to calculate the probability that the sample mean is less than 33.6 for both sample sizes? Yes No c. Calculate the above probabilities for both sample sizes. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) n Probability 41 82

Answer 1

Solution :

Given that ,

mean = = 33

standard deviation = = 2.1

a) n = 41

=   = 33

= / n = 2.1/ 41 = 0.328

n = 82

= / n = 2.1/ 82 = 0.232

b) yes, using standard normal distribution because original distribution is normal.

c) P( < 33.6) = P(( - ) / < (33.6 - 33) / 0.328)

= P(z < 1.83)

Using z table

= 0.9664

P( < 33.6) = P(( - ) / < (33.6 - 33) / 0.232)

= P(z < 2.59)

Using z table

= 0.9952