Question

Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S.      adults will try to pad their insurance claim this year. A director of an insurance adjustment office has just received 128 insurance claims to be processed. What is the probability that more than 80 of the claims are not padded?

Group of answer choices

26.7%

51.2%

25.1%

32%

28.1%

The mean temperature in downtown Los Angeles is 66.3 degrees Fahrenheit with a standard deviation of 8 degrees Fahrenheit. Assume that temperature readings are normally distributed.

Find the probability that the temperature in downtown L.A. is between 50.2 and 82.2 degrees Fahrenheit any given day.

Group of answer choices

0.9354

0.0076

0.9539

0.0222

0.9761

Answer 1

Q1). Proportion of padded claim= 0.4

Proportion of claim that are not padded, p = 0.6

Sample size, n = 128

Mean, µ = n*p = 128 * 0.6 = 76.8

Standard deviation, σ = √(n*p*(1-p)) = √(128 * 0.6 * 0.4) = 5.5426

Probability that more than 80 of the claims are not padded, P(X > 80) =

= P((X - µ)/σ > (80 - 76.8)/5.5426)

= P(z > 0.58)

= 1 - P(z < 0.58)

Using excel function:

= 1 - NORM.S.DIST(0.58, 1)

= 0.281 = 28.1%

Answer : 28.1%

-----------------------------

Q2). Population mean, µ = 66.3

Population standard deviation, σ = 8

Probability that the temperature in downtown L.A. is between 50.2 and 82.2, P(50.2 < X < 82.2) =

= P( (50.2-66.3)/8 < (X-µ)/σ < (82.2-66.3)/8 )

= P(-2.0125 < z < 1.9875)

= P(z < 1.9875) - P(z < -2.0125)

Using excel function:

= NORM.S.DIST(1.9875, 1) - NORM.S.DIST(-2.0125, 1)

= 0.9545

which is near to the value 0.9539

Answer : 0.9539