Question

Mattel Corporation produces a remote controlled car that requires ‘three AA batteries’. The mean life of these batteries in this product is 35 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours.

e. There is a 73 percent chance that the life of these batteries will be below _____ many hours?

f. At least 46 percent of the mean life of these batteries will be have ____________ hours?

g. The probability that 82 percent of sample mean/average life of these batteries will be symmetrically distributed between what two values around the population mean?

Answer 1

Solution:-

Mean = 35, S.D = 5.5

e) There is a 73 percent chance that the life of these batteries will be below 38.37 many hours.

p-value for the bottom 73% = 0.73

z-score for the p-value = 0.613

By applying normal distribution:-

x = 38.3715

f) At least 46 percent of the mean life of these batteries will be have 35.55 hours.

p-value for the top 46% = 1 - 0.46 = 0.54

z-score for the p-value = 0.10

By applying normal distribution:-

x = 35.55

g) The probability that 82 percent of sample mean/average life of these batteries will be symmetrically distributed between 27.63 and 42.37 hours around the population mean.

p-value for the middle 82% = 0.09 and 0.91

z-score for the p-value = + 1.341

By applying normal distribution:-

x₁ = 27.63

x₂ = 42.37