Question

A certain company manufactures precision thermometers that are supposed to give readings of 0.00° C at the freezing point of water. Tests on a large sample of these thermometers reveal that some give readings above 0.00° C and some give readings below 0.00° C. Suppose thermometer readings are approximately normally distributed with mean thermometer 0.00° C with a standard deviation of 1.00°. What is the thermometer reading that separates the top 4% of readings from the rest? Round your answer to two decimal places; add trailing zeros as needed. The thermometer reading that separates the top 4% of readings from the rest is [ThermHigh]° C .

Answer 1

Given that,

mean = = 0.00

standard deviation = =1.00

Using standard normal table,

P(Z > z) = 4%

= 1 - P(Z < z) = 0.04

= P(Z < z ) = 1 - 0.04

= P(Z < z ) = 0.96

= P(Z <1.75 ) = 0.96

z = 1.75 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.75*1.00+0.00

x= 1.75