1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable.

X 1 2 3 4 5 6 7

P(X) .23 .34 .18 .14 .07 .03 .01

2. Use the binomial formula to compute the probability of a student getting 7 correct answers on a 10 question Quiz, if the probability of answering any one question correctly is 0.87.

3. Submit your answers to the following binomial questions. You may use the appendix tables 5 to answer parts a and b. According to a government study,15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 5 live in poverty?

b) what is the probability that 2 or less live in poverty?

c) what is the expected number (mean) that live in poverty?

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 45,000 and a standard deviation of 3000. For any given game:

A) What is the probability that attendance is greater than 47,500?

B) What is the probability that attendance will be 45,000 or more?

C) What is the probability of attendance below 40,000?

D) What is the probability of attendance between 38,500 and 46,500?

E) What must the attendance be at the game, for that game's attendance to be in the top 5% of all games?

1. The quality control manager at a lightbulb factory needs to estimate the mean life of a new type of lightbulb. The population standard deviation is assumed to be 100 hours. A random sample of 60 lightbulbs shows a sample mean life of 350 hours. Construct and explain a 95% confidence interval estimate of the population mean life of the new lightbulb.

2. A stationary store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 25 greeting cards indicates a mean value of $1.67 and the sample standard deviation is $0.32. Assuming a normal distribution, construct and explain a 95% confidence interval estimate of the mean value of all greeting cards in the store's inventory.

3. A telephone company wants to estimate the porportion of households that would purchase an additional service line if it were made available at a substantially reduced cost. A random sample of 500 households is selected and the results indicate that 135 of the households would purchase the additional service. Construct and explain a 99% confidence interval estimate of the proportion of all households that would purchase the additional service.

Subject | Mathematics |

Due By (Pacific Time) | 06/15/2014 12:00 am |

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