Question

The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.3 cm.

A. Find the probability that an individual distance is greater than 218.00 cm.

B. Find the probability that the mean for 20 randomly selected distances is greater than 203.30 cm.

C. Why can the normal distribution be used in part b) even though the sample size does not exceed 30?

a. The probability is?

round to four decimal places

b. The probability is?

round to four decimal places

c. Choose one.

A The normal distribution can be used because the mean is large.

B The normal distribution can be used because the finite population correction factor is small.

C. The normal distribution can be used because the probability is less than 0.5.

D. The normal distribution can be used because the original population has a normal distribution.

Answer 1

a)

P(Y > 218) = P(Y - mean > 218 - mean)
                  = P( (Y - mean)/SD > (218 - mean)/SD
                  = P(Z > (218 - mean)/SD)
                  = P(Z > (218 - 205.5)/8.3)
                  = P(Z > 1.506)
                  = 1 - P(Z <= 1.506)
                  = 0.066

b)

Data given:
Mean = 205.5, SD/root(N) = 1.855936, P(Y > 203.3) = ?;

P(Y > 203.3) = P(Y - mean > 203.3 - mean)
                  = P( (Y - mean)/(SD/root(N)) > (203.3 - mean)/(SD/root(N))
                  = P(Z > (203.3 - mean)/(SD/root(N)))
                  = P(Z > (203.3 - 205.5)/1.855936)
                  = P(Z > -1.185)
                  = 1 - P(Z <= -1.185)
                  = 0.882

c) The normal distribution can be used because the original population has a normal distribution.