Question

Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 7 centimeters.

The percentage of heights less than 145 centimeters

The percentage of heights between 16t centimeters and 180 centimeters

Answer 1

a) 0.75%

b) 60.9%

Step-by-step explanation:

The heights of adult women are distributed normally with a mean(μ) = 162 centimetres and a standard deviation (σ) = 7 centimetres.

z score is a measure of the distance a raw score is from the mean in terms of standard deviation units. The z score is given by the equation:

`z=(x-\mu)/(\sigma) \\`.

a) The percentage of heights less than 145 centimetres. For x = 145 centimetres, the z score is:

`z=(x-\mu)/(\sigma) =(145-162)/(7)=-2.43`

P(x < 145) = P(z < -2.43) = 0.0075

The percentage of heights less than 145 centimetres is 0.75%

b) The percentage of heights between 165 centimetres and 180 centimetres

For x = 165 centimetres, the z score is:

`z=(x-\mu)/(\sigma) =(160-162)/(7)=-0.29`

For x = 180 centimetres, the z score is:

`z=(x-\mu)/(\sigma) =(180-162)/(7)=2.57`

P(160 < x < 180) = P(-0.29 < z < 2.57) = P(z < 2.57) - P(z < -0.29) = 0.9949 - 0.3859 = 0.609

The percentage of heights between 160 centimetres and 180 centimetres is 60.9%