Question 2. There is a type of candy such that the quantity of sugar X (measured in grams) in a randomly-selected piece of candy is normally distributed, with expected value u ten pieces of this candy on Halloween night. We are interested in calculating the probability that Hector consumed more than 200 grams of sugar, accurately. Which of the following is NOT true? = 22 and variance o? = 8. Suppose that Hector eats (a) We can not calculate the exact probability because n is not large enough (b) The expected amount of sugar consumed is 220 (c) The probability we are interested in is very close to 0.987 (d) 68% is the probability that Hector will be within one standard deviation of the expected total amount of sugar consumed.

В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.

3. An airline has a baggage weight limit of 50 lb. Suppose that the weight of the baggage checked by an individual passenger is a random variable x with a mean value of 49 lb. If 110 passengers will board a flight, what is the approximate probability that the mean weight for this sample of passengers will exceed the limit if the standard deviation of the baggage weight for this group is 23 lb. ? (Round your answer to three decimal places.)

2. Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that X is less than 9.66 is 0.67, then what is the standard deviation of X?

Suppose Y is normally distributed with mean = -3 and variance equal to 4. Find the probability that Y is less than or equal to -0.3. Hint, you must standardize the random variable. 0.9115 0.4602 0.5832 0.1

Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information? .8 .2 .82 .18 NONE OF THE OTHERS