1. The life of cell batteries is normally distributed with a mean of 81 hours an

Question

1. The life of cell batteries is normally distributed with a mean of 81 hours and a standard deviation of 19.3 hours. What is the maximum time (in hours) that the worst 13% of batteries last?          (2 decpl )

2. The HR manager of a large department store believes the number of resignations per week of casual staff at the store can be approximated by a normal distribution with a mean of 45 resignations per week and variance 61.9 (resignations per week)2 . From a large amount of historical data available on the HR database regarding weekly resignations of casuals, a sample of 52 weeks was selected. What must the value of the sample mean be so that only 15% of all possible sample means (of size 52) are less than this value? Give your answer correct to 2 decimal places.

Explanation / Answer

#1.
mean = 81 and sd = 19.3
z-value for the area of 0.13 to the left of the mean in a normal curve is -1.1264

Using central limit theorm,
x = 81 -1.1264*19.3
x = 59.2605

Ans: 59.26 hours

#2.
mean = 45 and sd = sqrt(61.9) = 7.8677
z-value for the area of 0.15 to the left of the mean in a normal curve is -1.0364

Using central limit theorm,
x = 45 -1.0364*7.8677/sqrt(52)
x = 43.8692

Ans: 43.87 weeks

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