Answer:
Probability that the calculator works properly for 74 months or more is 0.04 or 4%.
Step-by-step explanation:
We are given that the life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 8 months.
Firstly, Let X = life span of a calculator
The z score probability distribution for is given by;
Z = [tex]\frac{ X - \mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 60 months
[tex]\sigma[/tex] = standard deviation = 8 months
Probability that the calculator works properly for 74 months or more is given by = P(X [tex]\geq[/tex] 74 months)
P(X [tex]\geq[/tex] 74) = P( [tex]\frac{ X - \mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{74-60}{8}[/tex] ) = P(Z [tex]\geq[/tex] 1.75) = 1 - P(Z < 1.75)
= 1 - 0.95994 = 0.04
Therefore, probability that the calculator works properly for 74 months or more is 0.04 or 4%.
