15) Assume that the height of adult females in the United States is approximately normally distributed with a mean of 64.1 inches and a standard deviation of 2.86 inches. A sample of 8 such women is selected at random. Find the probability that the mean height of the sample is greater than 63.5 inches.
Round your answer to 4 decimal places.
Solution :
Given that ,
mean = = 64.1
standard deviation = = 2.86
n = 8
_{} = 64.1
_{} = / n = 2.86 / 8 = 1.0112
P( > 63.5) = 1 - P( < 63.5)
= 1 - P[( - _{} ) / _{} < (63.5 -64.1) /1.0112 ]
= 1 - P(z <-0.59 )
Using z table
= 1 - 0.2776
= 0.7224
probability= 0.7224
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