Question

a.) Men's heights are distributed as the normal distribution with a mean of 71 inches and a standard deviation of inches. Find the probability that a randomly selected man has a height between 69 inches and 73 inches.

b.) Men's heights are distributed as the normal distribution with a mean of 71 inches and a standard deviation of 3 inches. A random sample of 100 men is selected. Find the probability that the sample mean is greater than 70.75 inches. Find a such that P(x<a)=.25

Answer 1

1) we can see that

   =71,   =3

Now find the probability that selected men has height between 69 and 73. *P(69<x< 73)

P(69<x<73) = p((x-/ <Z < (x-/​​​​​​))

=p(69-71/3 <z< 73-71/3)

= p(-0.67 < Z < 0.67)

P(69<x<73) = 0.2486 + 0.2486

P(69 < x < 73) = 0.4972.

2) we can see that

=71

=3

n=100

To find p(x> 70.75).

P(x>70.75) = 0.5 + p(0 < Z < (x-/(/n)))

=0.5 + p(0<Z<(70.75-71/0.3))

= 0.5 + p(0<z<-0.83)

= 0.5 + 0.2967

P(x> 70.75) =0.7967.

Find that p(x<a) =0.25

Z= x-/

X = z +

X = 0.25 *3 + 71

X = 71.75