Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 69 inches and standard
deviation 6 inches.
(b) If a random sample of twenty-seven 18-year-old men is selected,
what is the probability that the mean height x is between
68 and 70 inches? (Round your answer to four decimal
places.)
Solution :
Given that,
mean =
= 69
standard deviation =
= 6
n = 27
=
= 69
=
/
n = 6 /
27 = 1.15
P(68 <
< 70)
= P[(68 - 69) / 1.15 < (
-
)
/
< (70 - 69) / 1.15)]
= P(-0.87 < Z < 0.87)
= P(Z < 0.87) - P(Z < -0.87)
Using z table,
= 0.8078 - 0.1922
= 0.6156
Get Answers For Free
Most questions answered within 1 hours.