Question

Lifetimes of a certain brand of lightbulbs is known to follow a right-skewed distribution with mean 24 months and standard deviation 2 months. Suppose that a sample of 41 lightbulbs is taken. What is the probability that the total lifetime of these bulbs is less than 975 months? Select one: a. 0.7580 b. Not enough information has been given to answer the question. c. 0.0000 d. 0.5160 e. 0.2420 f. 0.4840

Select one:

a. 0.7580

b. Not enough information has been given to answer the question.

c. 0.0000

d. 0.5160

e. 0.2420

f. 0.4840

Answer 1

Here, μ = 984, σ = 12.8063 and x = 975. We need to compute P(X <= 975). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (975 - 984)/12.8063 = -0.7

Therefore,
P(X <= 975) = P(z <= (975 - 984)/12.8063)
= P(z <= -0.7)
= 0.2420