Question

In: Statistics and Probability

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3...

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3 years, and standard deviation of 2.4 years.

If you randomly purchase 21 items, what is the probability that their mean life will be longer than 11 years? (Give answer to 4 decimal places.)

Solutions

Expert Solution

Solution :

Given that,

mean = = 10.3

standard deviation = = 2.4

n = 21

= 10.3

= / n = 2.4 21 = 0.5237

P ( > 11 )

= 1 - P ( < 11 )

= 1 - P ( - / ) < ( 11- 10.3 / 0.5237)

= 1 - P ( z < 0.7/ 0.5237 )

= 1 - P ( z < 1.34)

Using z table

= 1 - 0.9099

= 0.0901

Probability = 0.0901

orchestra answered 2 years ago
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