Answer:
a) 15.9%
b) 2.3%
Step-by-step explanation:
We solving using z score formula. This formula is given as:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Calculate the percent of batteries with a useful life of less than 45 months. (Round your answer to the nearest tenth percent.)
x = 45, μ = 48, σ = 3
z = 45 - 48/3
= -1
Probability value from Z-Table:
The probability of batteries with a useful life of less than 45 months so
P(x<45) = 0.15866
Converting to percentage
0.15866 × 100 = 15.866
Approximately to the nearest tenth of a percent = 15.9%
b. Calculate the percent of batteries that will last longer than 54 months. (Round your answer to the nearest tenth percent.)
x = 58, μ = 48, σ = 3
z = 58 - 48/3
= 2
Probability value from Z-Table:
P(x<54) = 0.97725
P(x>54) = 1 - P(x<54)
= 0.02275
The probability of batteries that will last longer than 54 months is 0.02275
Converting to percentage
0.02275 × 100
= 2.275%
Approximately to the nearest tenth of a percentage = 2.3%
