Question

The average age of passenger train cars is 19.4 years. If the distribution of ages is normal and 15% of the cars are older than 21.1 years, find the standard deviation. Round z-value calculations to 2 decimal places and final answer to 2 decimal places.

Answer 1

Solution:-

Given that,

mean = = 19.4

x = 21.1

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.04 ) = 0.85  

z = 1.04

Using z-score formula,

x = z * +

21.1 = 1.04 * + 19.4

  = 21.1 - 19.4 / 1.04

= 1.63