Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 0.7 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years?

Round answer to three decimal places

Answer 1

The probability of 6 years or more, so we want the complement,

1 - 0.98533 = 0.01467                        1.467% chance, not very likely.

What is Z-score?

A z score is a type of statistical measurement that gives an idea of how far a raw score is from the mean of a distribution. A z score is used in a z test for hypothesis testing.

Here, Because you are looking for the mean of a group of 7.8, the standard deviation will shrink by a factor of √6

Old standard deviation = 0.7,

new standard deviation = 0.7/√6 = 0.64254

You need to find a z-score and then convert your z-score to a probability.

z-score = (your score - average)/ std dev

z-score = (7.8 - 6)/0.64254

z-score = 2.1789

To convert a z-score either look it up on a table or use a calculator.

But z-tables are designed to shade to the left, which means this is the probability that the mean life is 6 years or less. We want the probability of 6 years or more, so we want the complement, 1 - 0.98533 = 0.01467

1.467% chance, not very likely.

Learn more about Z-score from:

brainly.com/question/15016913

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