The overhead reach distances of adult females are normally distributed with a me

Question

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8 cm. a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 195.30 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 as needed.) b. The probability is Round to four decimal places as needed.) c. Choose the correct answer below. 1S A· O B. ° C. O D. The normal distribution can be used because the mean is large. 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.

Explanation / Answer

Solution:

Normal Distribution
Mean = 197.5
Standard deviation = 8
Normal distribution Z = X - / ~ N(0,1)

a) P (X > 210 ) = P ( X > 210197.5/8)
= P ( Z > 1.56 ) = 0.0594
b) P(X > 195.3) = P ( X > 195.3197.5/8/sqrt(25))
= P ( Z > -1.3750 ) = 0.0846
c) c. The normal distribution can be used because the original population has a normal distribution.

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