Q1.The Chapin Social Insight Test evaluates how accurately the subject appraises

Question

Q1.The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

How high a score must you have in order to be in the top 20% of the population in social insight?

Q2.The household income in a certain community is normally distributed with a mean of $42,000 and a standard deviation of $5,000. The proportion of households with incomes between $46,000 and $50,000 is

Q3.

The number of people living on American farms has declined steadily during the past century. Here are data on the farm population (millions of persons) from 1935 to 1980:

Find the least squares regression equation of farm population on year. Hint: Use a computer or a graphing calculator to find equation.

Year 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 Population 32.1 31.5 28.4 29.0 23.1 21.6 18.4 15.7 13.9 12.2

Explanation / Answer

1)
mean = 25 , s = 5
z value at 20% = 0.8416
x = mean + z * s
= 25 + 0.8416 * 5
= 29.208

2)
mean = 42000 , s = 5000
p( 46000 < X < 50000)
P(X < 46000)
z = (x - mean) / s
= ( 46000 - 42000) / 5000
= 0.8

P(X < 50000)
z = (x - mean) / s
= ( 50000 - 42000) / 5000
= 1.6

P(46000 < X < 50000) = P( 0.8 < z < 1.6) = 0.1571

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