A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 16 years with a standard deviation of 5 years. If the claim is true, in a sample of 32 wall clocks, what is the probability that the mean clock life would be greater than 15.6 years? Round your answer to four decimal places.

0.6745 is the probability that the mean clock life would be greater than 15.6 years.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 16 years

Standard Deviation, σ = 15 years

Sample size, n = 32

Standard error due to sampling =

We assume that the distribution of clock life is a bell shaped distribution that is a normal distribution.

Formula:

P(mean clock life would be greater than 15.6 years)

P(x > 15.6)

Calculation the value from standard normal z table, we have,  

0.6745 is the probability that the mean clock life would be greater than 15.6 years.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47