The overhead reach distances of adult females are normally distributed with a mean of 202.5cm

and a standard deviation of 8.6cm.

a. Find the probability that an individual distance is greater than 215.00 cm.

b. Find the probability that the mean for 25 randomly selected distances is greater than 200.30cm.

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 4 decimal places)

b. The probability is ___________ (round to 4 decimal places)

c. choose the correct answer below:

• The normal distribution can be used because the probability is less than 0.5
• The normal distribution can be used because the original population has a normal distribution.
• The normal distribution can be used because the finite population correction factor is small.
• The normal distribution can be used because the mean is large.

Thank you.