The heights for 5-year-old boys follow the normal distribution with a mean height of 43 inches and a standard deviation of 5.3 inches. A sample of 60 boys is randomly selected.If possible, find the probability that the mean height of boys in the sample is higher than 42 inches. If not, explain.
= 43 inches
= 5.3 inches
For sampling distribution of mean for a sample of size n,
P( < A) =
P(Z < (A -
)/
)
n = 60
=
= 43 inches
=
=
= 0.6842
P(mean height of boys in the sample is higher than 42 inches) =
P( >
42)
= 1 - P( <
42)
= 1 - P(Z < (42 - 43)/0.6842)
= 1 - P(Z < -1.46)
= 1 - 0.0721
= 0.9279
The heights for 5-year-old boys follow the normal distribution with a mean height of 43 inches...
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