Question

Suppose X is a normal random variable with mean p = 49 and standard deviation o = 8. (a) Compute the z-value corresponding to X = 37. (b) Suppose the area under the standard normal curve to the left of the Z-value found in part (a) is 0.0668. What is the area under the normal curve to the left of X = 37? (c) What is the area under the normal curve to the right of X = 37?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 49

standard deviation = $\sigma$ =8

x =37

(A)z =( x -$\mu$) / $\sigma$ =37 - 49 / 8= -1.5

(B)P(x < 37) = P(( x -$\mu$) / $\sigma$ (37 - 49) /8 )

= P(z < -1.5)

Using z table

=0.0668   

(C)

P(x >37) = 1 - P(( x -$\mu$) / $\sigma$ (37 - 49) /8 )

= 1 - P(z < -1.5)

Using z table

=1 - 0.0668

=0.9332