Answer:
Probability that the mean clock life would be greater than 18 years is 0.04182 .
Step-by-step explanation:
We are given that the designer claims they have a mean life of 17 years with a standard deviation of 4 years.
Let X bar = mean clock life
The z score probability distribution is given by;
Z = [tex]\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean life = 17 years
[tex]\sigma[/tex] = standard deviation = 4 years
n = sample of wall clocks = 48
So, the probability that the mean clock life would be greater than 18 years is given by, P(X bar > 18 years);
P(X bar > 18) = P( [tex]\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{18 - 17}{\frac{4}{\sqrt{48} } }[/tex] ) = P(Z > 1.73) = 1 - P(Z <= 1.73)
= 1 - 0.95818 = 0.04182
Therefore, the probability that the mean clock life would be greater than 18 years is 0.04182 .
