The set of life spans of an appliance is normally distributed with a mean mc013-1.jpg = 48 months and a standard deviation mc013-2.jpg = 8 months. What is the life span of an appliance that has a z-score of –3?

The life span would be 24 months.

The formula for z-scores is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]

Using the information we're given we have:
[tex]-3=\frac{X-48}{8}[/tex]

Multiply both sides by 8 to cancel it:
-3(8) = ((X-48)/8)*8
-24 = X-48

Add 48 to both sides:
-24+48 = X-48+48
24=X

Answer Link

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-04T17:42:04+02:00

The life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.

What is Z-test?

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

We have:

Z = -3,

[tex]\rm \mu = 48[/tex]

[tex]\sigma = 8[/tex]

We know the formula for the Z-score:

[tex]\rm Z = \frac{X-\mu}{\sigma}[/tex]

[tex]\rm-3= \frac{X-48}{8}[/tex]

-24 = X - 48

X = 24 months

Thus, the life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.

Learn more about the Z-test here:

brainly.com/question/15683598

#SPJ3