I need help with a problem from my statistics homework. I don't understand this...

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.1 years, and standard deviation of 0.7 years.

If you randomly purchase one item, what is the probability it will last longer than 5 years?

Answer 1

So if you just standardize the normal random variable, you can then just look it up in the Z-Table. The standardized form is

Z = (x - mean) / St. Dev

So, Z = (5 - 4.1) / 0.7

Z= 1.2857

Depending on how your professor prefers you to round, you will either have a Z-score of 1.28 or 1.29.

The Z-score of 1.29 shows a probability of .9015 on the Z-table. The question asks for the probability that the item will last longer than 5 years. At 5 years, the probability is .9015. So, to find out the probability of it lasting more than 5 years, we just subtract it from 1.

P(x>5) = 1 - .9015

P(x>5) = .0985

Answer 2

Hello Sarah,

You need to tell us whether you use a table, a statistical calculator, or computer software to solve this problem and the other one that you submitted.

In my class, we use a TI-83 or 84 calculator. You would press the DIST key and choose normalcdf(

After that, you must enter 4 numbers and the other parenthesis.The format is

normalcdf(lower bound, upper bound, mean, standard deviation)

Since it says longer than 5 years, you want numbers that are 5 or more. There is no upper bound given, so just use a very large number such as 1000.

See if you can finish this and the other problem you asked. If you don't use calculators, you may resubmit the question for an Expert to give you help.