Respuesta :
Answer:
Probability that average height would be shorter than 63 inches = 0.30854 .
Step-by-step explanation:
We are given that the average height of 20-year-old American women is normally distributed with a mean of 64 inches and standard deviation of 4 inches.
Also, a random sample of 4 women from this population is taken and their average height is computed.
Let X bar = Average height
The z score probability distribution for average height is given by;
Z = [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 64 inches
[tex]\sigma[/tex] = standard deviation = 4 inches
n = sample of women = 4
So, Probability that average height would be shorter than 63 inches is given by = P(X bar < 63 inches)
P(X bar < 63) = P( [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{63-64}{\frac{4}{\sqrt{4} } }[/tex] ) = P(Z < -0.5) = 1 - P(Z <= 0.5)
= 1 - 0.69146 = 0.30854
Hence, it is 30.85% likely that average height would be shorter than 63 inches.
