Question

The length of time it takes to find a parking space at 8am follows a normal distribution with a mean of 10 minutes and a standard deviation of 3 minutes. Calculate the interquartile range.

Answer 1

Solution:-

Given that,

mean = = 10

standard deviation = =3

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.67 ) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 3+10

x = 7.99

First quartile =Q1 = 7.99

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 3+10

x = 12.01

Third quartile =Q3 = 12.01

IQR = Q3 - Q1=12.01-7.99=4.02