Statistics and Probability Answers

2. Consider the population consisting of the values (1, 2, 8). List all possible samples of size 2 which can be drawn without replacement from the population. Find the following:

a. Population mean

b. Population variance

c. Population standard deviation

d. Mean of the samples and mean of the sampling distribution of mean

e. Variance of the sampling distribution of means

f. Standard deviation of the sampling distribution of means

The cashier of a fastfood restaurant claims that the average amount spent by customers for dinner is P 120. 00. A sample

of 50 customers over a month period was randomly selected and it was found out that the average amount spent for dinner

was P 112. 50. Using a 0.05 level of significance, can it be concluded that the average amount spent by customers is more

than P 120. 00? Assume that the population standard deviation is P 6.50. (Use Critical Value Method)

suppose that during any hour in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. what is the probability that a random sample of 49 different shopping hours will yield a sample mean between 441 and 446 shoppers?

The weights (in kg) of 11 Stem B follow a normal distribution and has a mean of 52 and a standard deviation of 4. How many students have weights greater than 56?

Americans ate an average of 25.7 pounds of confectionery products each last year and

spent an average of $61.50 per person doing so. If the standard deviation of consumption is 3.75 pounds and the standard deviation of the amount spent is %5.89, find the following:

a. The probability that the sample mean confectionary consumption for a random sample

of 40 American consumers was greater than 27 pounds.

b. The probability that for a random sample of 50, the sample mean for confectionary

spending exceeded $60.00

The average per capita spending on health care in United States is $5274. If the standard

deviation is $600 and the distribution of health care spending is approximately normal, what is the probability that a randomly selected person spends more than $6000? Find the limits of the middle 50% of individual health care expenditures.

a company produces mosquito repellents that have a period of effectiveness that is approximately normally distributed with a mean of 300 hours and a standard deviation of 30 hours. A sample of 40 repellents was taken and the average period of effectiveness is computed as 290 hours. Test the hypothesis that µ = 300 against the alternative that µ ≠ 300

Four cards are drawn from a desk without replacement. Find these probabilities.

a. All cards are jacks.

b. All cards are black cards.

c. All cards are hearts.

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25% test at 99% confidence level

How does the t-distribution differ from a normal distribution? A. The t-distribution has a mean of 0. B. The t-distribution has a thicker tail. C. The t-distribution is symmetric in the middle. D. The t-distribution is bell-shaped.