thermometer reading

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.)

Answer 1

We seek the thermometer reading that delineates the largest 4% of a normal distribution with a mean of mu = 0.00 and a standard deviation of sigma = 1.00.

The z statistic is

z = (x - mu)/sigma, the number of standard deviations by which x differs from mu.

The cumulative normal distribution has its 96%tile (thus only 4% of the values are larger) when

z = 1.74, so we can calculate the corresponding temperature from

x = (sigma) (1.74) + mu = (1)(1.74) + 0 = 1.74 oC