Question

Let X be normallyh distributed with a mean of 100 and standard deviation of 25 a)what is the probability that X will be at most 120 b)suppose a sample of 30 students were selected,what is the probability that X will be more than 95

Answer 1

(a)

=mean = 100

= SD = 25

P(X120):

Z = (120 - 100)/25= 0.8

Table of Area Under Standard Normal Curve gives area = 0.2881

So,

P(X120) = 0.5 + 0.2881 = 0.7881

So,

Answer is:

0.7881

(b)

n = 30

SE = /

= 25/ = 4.5644

To find P(>95):

Z = (95 - 100)/4.5644 = - 1.0954

Table gives area = 0.3643

So,

P( > 95) = 0.5 + 0.3643 = 0.8643

So,

Answer is:

0.8643