Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₂₅, the 25-percentile. This is the temperature reading separating the bottom 25% from the top 75%.

Answer 1

Given that,

mean = = 0

standard deviation = = 1

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z <-0.67 ) = 0.25

z = -0.67 Using standard normal z table,

Using z-score formula  

x= z * +

x=-0.67 *1+0

x= -0.67