Question

You take a random sample of 500 people from the city of Salinas and find that their average income is $45,000 per year with a standard deviation of $10,000; also assume that income for Salinas community is normally distributed, and that you have excluded extreme data points or outliers from your sample:

Approximately how many people in your sample make less than $35,000 per year?

Approximately how many people in your sample make between $25,000 and $55,000?

Answer 1

For normal distribution, P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = $45,000

Standard deviation = $10,000

P(a person will have salary less than $35,000) = P(X < 35,000)

= P(Z < (35,000 - 45,000)/10,000)

= P(Z < -1)

= 0.1587

Number of people in sample of 500 that make less than $35,000 = 0.1587x500

= 79.35

= 79 people

P(a person will have salary between $25,000 and $55,000) = P(25,000 < X < 55,000)

= P(X < 55,000) - P(X < 25,000)

= P(Z < (55,000 - 45,000)/10,000) - P(Z < (25,000 - 45,000)/10,000)

= P(Z < 1) - P(Z < -2)

= 0.8413 - 0.0228

= 0.8185

Number of people in sample of 500 that make salary between $25,000 and $55,000 = 0.8185x500

= 409.25

= 409 people