Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes of the Duxcell batteries are 10 and 2 minutes respectively, the mean and standard deviation for the Infinitycell batteries are 14 and 3 minutes respectively.

Part a) What is the probability that a Duxcell battery will last longer than an Infinitycell battery?,

Question

Mathematics

Jeffrey Reid

11 December, 13:33

Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes of the Duxcell batteries are 10 and 2 minutes respectively, the mean and standard deviation for the Infinitycell batteries are 14 and 3 minutes respectively.

Part a) What is the probability that a Duxcell battery will last longer than an Infinitycell battery?,

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Answers (1)

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Gummi Bear · Answer 1

Solution:

X = N (10, 2^2)

This means that:

mean is 10

variance is 2^2

Y = N (14, 3^2).

Asked:P (X > Y)

= P (X - Y > 0).

mean of Z = X - Y

= 10 - 14

variance = 2^2 + 3^2

Z = N (-4, 2^2 + 3^2).