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In: Statistics and Probability

Salaries for new assistant professors at State College are normally distributed with a mean of $50000...

Salaries for new assistant professors at State College are normally distributed with a mean of $50000 and a standard deviation of $6000 . We randomly survey 10 teachers from that district, let X be the salary of a randomly selected teacher at State, and let X¯ be the average salary of 10 randomly selected teachers.

(2%) X∼ (
,
) .

(3%) X¯∼ (
,
) .

(3%) Find the probability that an individual teacher earns more than $65,000.

P(X>65000)=   

(3%) Find the probability that the average salary for the sample is more than $65,000.

P(X¯>65000)=   

(3%) Find the 90th percentile for the average teachers’ salary for samples of 10 teachers.

If P(X¯<a)=0.9 then a=   
.

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orchestra answered 2 years ago
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