Statistics and Probability Answers

1. The number of accidents in a production facility has a Poisson distribution with a mean of 2.7 per month. For a given month, what is the probability that there will be more than three (3) accidents?

Four coins are tossed at once. Let Y be the random variable representing the number of

heads that occur.

Assumed that the fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content (1.90 liters, in this case), the manufacturer may be subject to a penalty by the state office of consumer affairs. Bottles that have a net content above 2.10 liters may cause excess spillage upon opening. What proportion of the bottles will contain (a) between 1.90 and 2.00 liters? (b) between 1.90 and 2.10 liters? (c) below 1.90 liters or above 2.10 liters? (d) At least how much soft drink is contained in 99% of the bottles? (e) 99% of the bottles contain an amount that is between which two values(symmetrically distributed) around the mean?

The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. (a) What proportion of the population watches television for more than 7 hours per day? (b) What is the probability that the average number of hours spent watching television by a random sample of five adults is more than 7 hours? (c) What is the probability that in a random sample of five adults all watch television for more than 7 hours per day?

The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. (30%) (a) What proportion of the population watches television for more than 7 hours per day? (b) What is the probability that the average number of hours spent watching television by a random sample of five adults is more than 7 hours? (c) What is the probability that in a random sample of five adults all watch television for more than 7 hours per day? 

A subdivision household collects an 20 killos of trash each week. If the standard deviation is 3.5 kilos based on the assumption that the data collected are normally distributed, find the probability that a household selected at random collect trash of:

a. lower than 16 kilos

b. greater than 22.5 kilos

c. between 14 kilos and 23.5 kilos

d. 11 kilos and 15 kilos

You pay 168 dollars to play a lottery. A bin contains 91 balls labeled from 1 to 91. You draw a ball and you receive cash in the amount of 3 times the number shown on the ball. Let X be the number shown on the ball.

(a) Identify the probability distribution for the X.

Distribution = Parameter =    

(b) Calculate the probability that you get more money back than you have spent on the ticket.

P(you win) =    

(c) Calculate the average number that you will draw. Calculate the standard deviation for this number.

μ =    

σ =    

(d) Calculate the average amount that you will gain (winnings minus what you paid) by purchasing a ticket. Calculate the standard deviation associated to this number.

Average Gain (Winnings - paid) =    

SD of Gain =    

The following simple random sample was selected from a normal distribution: 4, 6, 3, 5, 9, and 3.

a.     Construct a 90% confidence interval for the population mean μ.

b.    Construct a 95% confidence interval for the population mean μ.

c.     Construct a 99% confidence interval for the population mean μ.

A student obtained a score of 45 in Math and a score of 60 in Science. If the mean and standard deviation of the math scores are 26.4 and 7.2, respectively, while that of science are 42.5 and 12.6,

The latest nationwide political poll indicates that for Indians who

are randomly selected, the probability that they are with alliance

ABC is 0.55, the probability that they are with alliance PQR is

0.30 and the probability that they are with alliance XYZ is 0.15.

Answer the following questions pertaining to a randomly chosen

group of 10 Indians.

What is the probabilities:

(i) None are with alliance ABC ?

(ii) 2 are with alliance XYZ ?

(iii) At least 8 are with alliance PQR ?