A certain standardized test has scores which range from 0 to 500, with decimal s

Question

A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 318 and a standard deviation of 45.

Find the percentile P87 for the scores of students taking the exam.

Round your answer to 2 decimal places.

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The mean salary of people living in a certain city is $37500 with a standard deviation of $2322. A sample of 53 people is selected at random from those living in the city.

Find the probability that the mean income of the sample is within $500 of the population mean.

Round your answer to 4 decimal places.

Explanation / Answer

Mean ( u ) =318
Standard Deviation ( sd )=45
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.87
Value of z to the cumulative probability of 0.87 from normal table is 1.126
P( x-u/s.d < x - 318/45 ) = 0.87
That is, ( x - 318/45 ) = 1.13
--> x = 1.13 * 45 + 318 = 368.6876 ~ 368.67   

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