Question

I honestly don't know how to solve it please help me. A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. What is the probability that a CD will last less than 3 years?

1.11%
10.56%
86.65%
100%

Answer 1

10.56 is the correct answer.

Answer 2

10.56 %

Explanation:

Information:

mean = 4 years

standard deviation = 0.8 years

P(x < 3) = ?

using the normal distribution you must follow these steps to calculate P(x < 3):

• you calculate Z with this formula:

Z=(x - μ)/(σ/
`√(n)`)

where:

x is the raw measurement

μ is the mean

σ is the standard deviation

n is the size of sample

in this case, x = 3 , μ = 4, σ = 0.8, n = 1.

thus:

`Z = ((3-4))/((0.8)/(√(1)))\\\\Z = -(1)/(0.8)\\\\Z = -1.25\\`

from the table of normal distribution attached, we see that our Z value is 0.1056

P(x < 3) = 0.1056

so the probability that a CD will last less than 3 years is 10.56%