Question

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 110 and a standard deviation of 13. What is the probability that a student selected at random will have the following IQs? (Round your answers to four decimal places.)

(a) 140 or higher

(b) 115 or higher

(c) between 110 and 115

(d) 100 or less

Answer 1

= 110, = 13

a)  n=1, P(x 140 )=?

z= 2.31

P(x 140) = 1 - P(z < 2.31)

find P(z < 2.30) using z table

P(z < 2.31) = 0.9895

P(x 140) = 1 - 0.9895

P(x 140) = 0.0105

probability of 140 or higher = 0.0105

b)

n=1, P(x 115 )=?

z= 0.3846

Z= 0.38

P(x 115) = 1 - P(z < 0.38)

find P(z < 0.38) using z table

P(z < 0.38) = 0.6497

P(x 115) = 1 - 0.6497

P(x 115) =  0.3503

probability of 115 or higher =  0.3503

c)

n=1, P(110x 115 )=?

P(110x 115 )= P(x 115 ) - P(x 110)

first find P(x 115 )

z= 0.3846

Z= 0.38

P(x 115) = P(z < 0.38)

find P(z < 0.38) using z table

P(z < 0.38) = 0.6497

P(x 115) =  0.6497

now find P(x 110)

z= 0

P(x 110) = P(z < 0)

find P(z < 0) using z table

P(z < 0) = 0.5

P(x 110) =  0.5

P(110x 115 )= P(x 115 ) - P(x 110)

P(110x 115 )= 0.6497−0.5

P(110x 115 )= 0.1497

Probability of between 110 and 115 =  0.1497

d)

n=1, P(x 100 )=?

z= −0.7692

Z= - 0.77

P(x 100) = P(z < -0.77)

find P(z < -0.77) using z table

P(z < -0.77) = 0.2209

P(x 100) =  0.2209

probability of 100 or less =  0.2209