Answer:
The probability that they have a mean height greater than 67.8 inches is 0.00212.
Step-by-step explanation:
We are given that the heights of men are normally distributed with a mean of 66.8 inches and a standard deviation of 2.8 inches.
64 men are randomly selected.
<em>Let </em><em> = sample mean height </em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = mean height = 66.8 inches
= standard deviation = 2.8 inches
n = sample of men = 64
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that they have a mean height greater than 67.8 inches is given by = P( > 67.8 inches)
P( > 67.8) = P( > ) = P(Z > 2.86) = 1 - P(Z 2.86)
= 1 - 0.99788 = 0.00212
<em>The above probability is calculated by looking at the value of x = 2.86 in the z table which has an area of 0.99788.</em>
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Therefore, if 64 men are randomly selected, the probability that they have a mean height greater than 67.8 inches is 0.00212.