Question

Heights of women are normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches.

a) find the probability that the height of a single randomly chosen women is less than 62 inches

b) find the probability that the mean height of a sample of 16 women is less than 62 inches

Answer 1

Solution :

Given that ,

mean =   = 63.8

standard deviation = σ   = 2.6

(A)n = 1

= 63.8

=  / n = 2.6 / 1=2.6

P( < 62) = P[( - ) / < (62-63.8) /2.6 ]

= P(z <-0.69 )

Using z table  

= 0.2451   

probability= 0.2451

(B)

n = 16

= 63.8

=  / n = 2.6 / 16=0.65

P( < 62) = P[( - ) / < (62-63.8) /0.65 ]

= P(z <-2.77)

Using z table  

= 0.0028   

probability= 0.0028