The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.

The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.

Find the probability that a record player will last less than 2 years?

the  probability that a record player will last less than 2 years is 0.1586

Step-by-step explanation:

Given that:

A mean which is normally distributed = 3

and a standard deviation = 1

The objective is to find that a record player will last less than 2 years

Let X be the random variable

i.e

From the standard normal tables :

P(X < 2) = 0.1586

Therefore; the  probability that a record player will last less than 2 years is 0.1586

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240