Statistics and Probability Answers

The annual rainfall in a certain area is normally distributed with a mean of 25 inches and a standard deviation of 5 inches. The following questions ask you to compute probabilities and quintiles from a normal distribution.
a. What is the probability the area receives at least 30 inches of rain in a year?
b. What is the probability the area receives between 15 and 30 inches of rain in a year?
c. What is the probability the area receives at most 20 inches of rain in a year?

Ecobank Ghana issues its own credit card. The credit manager, Giovina wants to find whether the mean monthly unpaid balance is not at most Ghc400. The level of significance is set at 0.05. A random check of 25 unpaid balances revealed that the average is GHc410 with the standard deviation of GHc20. Should the credit manager conclude that the population mean is not at most GHc400, or is it reasonable that the difference is due to chance? a. Explain why t is the test statistic to be used here. b. What is the critical value of the test statistic?

c. What is your decision regarding the H0? d. Estimate the p-value and use it to decide. e. Should the credit manager conclude that the population mean is not at most GHc400, or is it reasonable that the difference is due to chance? Explain briefly

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.1. Suppose you purchase box after box until you have obtained four of these prizes.

(a)
What is the probability that you purchase x boxes that do not have the desired prize?
h(x; 4, 0.1)
b(x; 4, 1, 10)
h(x; 4, 1, 10)
b(x; 4, 0.1)
nb(x; 4, 1, 10)
nb(x; 4, 0.1)


(b)
What is the probability that you purchase six boxes? (Round your answer to four decimal places.)

(c)
What is the probability that you purchase at most six boxes? (Round your answer to four decimal places.)

(d)
How many boxes without the desired prize do you expect to purchase?

How many boxes do you expect to purchase?

P(X = x) = k/x+1; where x=1,2,3
Evaluate k.

We roll two six-sided fair dice and let X be the randorn variable corresponding to the maximum value.

1. Compute X(s) for all s in S.

2. Write a formula for PX E B), for any subset B of the real numbers.

. Set up a 95% confidence interval estimate for the population mean, based on each of the
following sets of data, assuming that the population is normally distributed:
Set 1: 1, 1, 1, 1, 8, 8, 8, 8
Set 2: 1, 2, 3, 4, 5, 6, 7, 8
Explain why these data sets have different confidence intervals even though they have the
same mean and range.

You use a line of best fit for a set of data to make a prediction about unknown value. The correlation coefficient for your data set is 0.984. How confident can you be that your predicted value will be reasonably close to the actual value.

Weights. If the weights of 600 students are normally distributed with a mean of 50 kilograms and a variance of 16 kilograms
a. Determine the percentage of students with weights lower than 55 kilograms.
b. How many students have weights exceeding 52 kilograms?

Based on a random sample of 600 families in a city, we found 396 of them have at least one child.
a) Construct a 77% confidence interval on the percentage of families in the city which have at least one child and give the confidence statement.
b) With a 92% confidence, suppose we wish to control the confidence interval to be within 1% of the population proportion. What is the minimum sample size that we need to use to achieve this?