Gestation periods of humans have a mean of 266 days and a standard deviation of

Question

Gestation periods of humans have a mean of 266 days and a standard deviation of 16 days. Let y denote the variable "gestation period" for humans.

a. Find the standardized variable corresponding to y.
b. What are the mean and standard deviation of the standardized variable?
c. Obtain the z-scores for gestation periods of 227 days and 315 days. Round your answers to two decimal places.
d. Interpret your answers in part (c).
e. Construct a graph similar to Fig. 3.16 on page 143 that shows your results from parts (b) and (c).

Explanation / Answer

a. ANSWER: z = (x - )/ z = STANDARDIZED VARIABLE FOR NORMAL DISTRIBUTION

b. ANSWER: Mean = 266 days; Standard Deviation = 16 days

c. ANSWER: z = -2.44; z = 3.06

Why??
COMPUTATION OF STANDARDIZED VARIABLE z
277 days: z = (227 - 266) /16 = -2.44
315 days: z = (315 - 266) / 16 = 3.06


d. ANSWER: Probabality (nearly) 100% gestation period is between 227 and 315 days.

Why??

227 days: P (z -2.44) = 0.007
315 days: P(z 3.06) = 0.999

P(-2.44 z 3.06) = 0.999 - 0.007 = (nearly) 1.00 (100% Confidence Interval)

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