The weekly incomes of a large group of sales clerks are normally distributed wit

Question

The weekly incomes of a large group of sales clerks are normally distributed with a mean of $1000 and a standard deviation of $125. Use the normal distribution to calculate the following:

What is the probability that the income is less than $800?

What percent of weekly income is more than $1200?

What is the probability that the income is between $900 and $1,200?

Find the income that represents the 50thpercentile.

Find the income that represents the 90thpercentile.

5% of the incomes are below what value?

The top 5% of the incomes are above what value?

Between which two values will the middle 50% of the data lie?

A. What percent of income lies within $250 of the population mean?

B.  68% of observations lie within which two values?

C.  What percent of income lies within $375 of the population mean?

D.  Discuss how your answers in A-C compare to the Empirical Rule.

Consider a sample with a mean of 30 and a standard deviation of 5.  Use Chebyshev’s Theorem to find the percent of data that lies within the data range of 15 and 45?

Explanation / Answer

a) P(Z<(800-1000)/125

= P(z<-1.6)

= 0.0548

b) P(z>(1200-1000)/125

= P(z>1.6)

= 0.0548

c) P((900-1000)/125<z<(1200-1000)/125

= P(-0.8<z<1.6)

= 0.7333

d) 50th Percentile = 0*125+1000 = $1000

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