Question

1. The average height of adult females in the United States is 64.5 inches. Assume that σ = 2.8 inches and the distribution is approx. normal.
   1. Find the probability that a female selected at random is taller than 66 inches.
   2. If a sample of 25 females is selected, find the probability that their mean height would be taller than 66 inches.
   3. Which probability is smaller? What can you say about the variability of the average of sample vs. the variability of a single observation?

Answer 1

Solution :

Given that ,

mean = = 64.5

standard deviation = = 2.8

(A)P(x > 66) = 1 - P(x < 66)

= 1 - P[(x - ) / < (66 - 64.5) /2.8 ]

= 1 - P(z < 0.54)

Using z table,

= 1 -0.7054

=0.2946

(B)n = 25

= 64.5

= / n = 2.8 / 25 = 0.56

P( > 66) = 1 - P( < 66)

= 1 - P[( - ) / < (66 - 64.5) /0.56 ]

= 1 - P(z <2.68 )

Using z table,    

= 1 - 0.9963

= 0.0037

part B probability is smaller