In a​ lottery, you bet on a six-digit number between 000000 and 111111. For a​ $1 bet, you win ​$700,000 if you are correct. The mean and standard deviation of the probability distribution for the lottery winnings are μ=0.70 (that is, 70 cents) and σ=700.00. Joan figures that if she plays enough times every​ day, eventually she will strike it​ rich, by the law of large numbers. Over the course of several​ years, she plays 1 million times. Let x denote her average winnings.

a. Find the mean and standard deviation of the sampling distribution of x

b. About how likely is it that Joan​'s average winnings exceed​ $1, the amount she paid to play each​ time? Use the central limit theorem to find an approximate answer.

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 105. What is the probability that the sample proportion will be within 10 percent of the population proportion?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =  (Enter your answer as a number accurate to 4 decimal places.)

A shopkeeper hires vacuum cleaners to the general public at 5$ per day. The mean daily demand is 2.6. Suppose the demand follows Poisson distribution. (a) Calculate the expected daily income from this activity assuming an unlimited number of vacuum cleaners is available (b) Find the probability that the demand on a particular day is: 0, exactly 1, exactly 2, exactly 3 or more than 3; (c) If only 3 vacuum cleaners are available for hire calculate the mean of the daily income. A nearby large store is willing to lend vacuum cleaners at short notice to the shopkeeper, so that she is able to meet the demand. However, this shop will charge £2 per day for this service regardless of how many, if any, cleaners are borrowed. Would you advice the shopkeeper to take this offer?

1. Solve the problem using the employment information in the table on Alpha Corporation

1. The mean of a set of data is 5.07 and its standard deviation is 3.39. Find the z-score for a value of 9.65. _______________________
2. Which is better and corresponds to the higher relative position, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? ____________________________________
3. On a given registration day, 45 CJ majors and 25 CIS majors arrive. What is the empirical probability that the next student to arrive will be a CJ major? ______________________________

No Hand Writing please, Type your answer.

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 198. What is the probability that the sample proportion will be within 4 percent of the population proportion?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =  

(Enter your answer as a number accurate to 4 decimal places.)

Chemical signals of mice.Consider Refer to the Cell (May 14, 2010) study of the ability of a mouse to recognize the odor of a potential predator, Exercise 3.63 (p. 143). Recall that theThe sources of these odors are typically major urinary ­proteins (Mups). In an experiment, 40% of lab mice cells exposed to chemically produced cat Mups responded positively (i.e., recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively. Explain why the probability distribution of x can be ­approximated by the binomial distribution. Find E(x) and interpret its value, practically. Find the variance of x. Give an interval that is likely to contain the value of x.

The ability of a mouse to recognize the odor of a potential predator is essential to the mouse’s survival. Typically, the source of these odors are major urinary proteins (Mups). 30% of lab mice sells exposed to chemically produced cat Mups responded positively (i.e. recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat MUPS. Let X represents the number of cells that respond positively.

a) Explain why the probability distribution of X can be approximated by the binomial distribution.

b) Find E(X) and interpret its value, practically.

c) Find the variance of X.

d) Give an interval that is likely to contain the value of X (2 st. dev around the mean).

e) How likely is it that less than half of the cells respond positively to cat Mups?

A local car dealer closes on Sundays at 6:00 pm. He counts the number

of cars available at that time. If there are two or less, order enough to

raise the level to six. Cars are delivered at night and are available when

the exhibition hall opens at 9:00 a.m. on Monday morning. Let Pd (x) be

the probability that the demand during the week is equal to x: Suppose that:

Pd (0) = 0.2 ,Pd (1) = 0.5 ,Pd (2) = 0.2 ,Pd (3) = 0.1

If there is more demand than cars during the week than those available at the

start of it, the excess demand is wasted and the distributor ends the week with

zero cars available. Define a markov chain where states are numbers of cars

available on Monday morning at 9:00 am. Find the transition matrix.

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.772, and the probability of buying a movie ticket without a popcorn coupon is 0.228. If you buy 15 movie tickets, we want to know the probability that more than 10 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)