Probability problems for binomial and normal variable

1.) Listed below is the percent increase in sales for the MG Corporation over the last 5 years. Determine the geometric mean percent increase in sales over the period. (See attached)

2.) In 1996 a total of 14,968,000 taxpayers in the United States filed their individual tax returns electronically. By the year 2002 the number increased to 46,282,200. What is the geometric mean annual increase for the period?

3.) The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

4.) A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:
a. The probability of making exactly four sales.
b. The probability of making no sales.
c. The probability of making exactly two sales.
d. The mean number of sales in the two-hour period.

5.) In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomialprobability as a normalprobability using the continuity correction.
BinomialProbabilityNormalProbability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomialprobability?

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95.
Can Nathan use the normal curve area to approximate a binomialprobability?

Answer the following:
(A) Find the binomialprobability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomialprobability P(x is at most 6) using probability notation.
(C) How would you find the normal approximation to the binomialprobability P(x = 6) in part A? Please show how you would calculate

h-p is said to be the leading seller of pc's in the U.S WITH 27% share of the pc market. if a researcher selects 130 recent pc purchases, use the normal approximation to the binomial to find the probability that more than 39 bought a h-p computer

The probability that an appliance is in repair is .6. If an apartment complex has 100 such appliances, what is the probability that at least 70 will be in repair? Using the normal approximation to the binomial.

Answer the following:
(A) Find the binomialprobability P(x = 4), where n = 12 and p = 0.50.
(B) Set up, without solving, the binomialprobability P(x is at most 4) using probability notation.
(C) How would you find the normal approximation to the binomialprobability P(x = 4) in part A? Please show how you would calculate

Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5.
Find the probability that x = 2 using the binomial tables.
Use the normal approximation to find the probability that x = 2

Assume that 12 percent of adults in this country have filed for bankruptcy at some point in their life. If an independent sample of 20 adults is selected find the probability that fewer than 5 will have filed for bankruptcy at some point in their life.

Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be re-worked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming, what is the (approximate) probability that X is:
a. At most 30
b. Less than 30