Question

Heights of fourth graders are Normally distributed with a mean of 52 inches and a standard deviation of 3.5 inches. What percentage of fourth graders are between 50 inches and 56 inches? A. 68.13% B. 27.42% C. 59.01% D. 95.27% E. 86.43%

Answer 1

= 52, =3.5

we want to find P(50 X 56 )

P(50 X 56 ) = P(X 56) - P(X 50)

first find P(X 56)

z =1.14

P(x 56) = P(z < 1.14)

find P(z < 1.1429) using normal z table we get

P(z < 1.1429)= 0.8735

P(x 56) =  0.8735

now find   P(X 50)

z = −0.5714

P(x 50) = P(z < −0.5714)

find P(z < −0.5714) using normal z table we get

P(z < −0.5714)= 0.2839

P(x 50) = 0.2839

now

P(56 X 50) = P(X 56) - P(X 50)

P(56 X 50) = 0.8735−0.2839

P(56 X 50) = 0.5896 =59.01

Answer= 59.01 %