Statistics and Probability Answers

3 A recent survey by a local municipality established that daily water usage by its households is normally distributed with a mean of 220 liters and a standard deviation of 45 liters.

(i) What percentage of households is likely to use more than 300 liters of water per day?

(ii) What is the probability of finding a household that uses less than 100 liters of water per day?

(iii) What percentage of households is likely to use between 300 to 350 liters of water per day?

A market researcher at a major company classified households by car ownership. The relative frequencies of households for each category of ownership are shown in Table 1.

Table 1. The relative frequencies of households

Number of cars House hold 0 1 2 3 4 5

Relative Frequency 0.1 0.3 0.4 0.12 0.06 0.02

Calculate the mean value and standard deviation of the random variable and interpret the result.

There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 3?

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed. What type of test does the problem represent?

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed. Which of the following is correct null and alternative hypothesis, in symbol?

The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, and the standard deviation is 35 mg. Assume the variable is normally distributed.

a. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 690?

b. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 690 mg?

c. Why is the probability in part A larger than part B? 

A. A researcher reports that the average salary of College Deans is more than $63,000. At a = 0.01 level of confidence, test the claim that the College Deans earn more than $63,000 a month.

Professor Balenciaga has reported her students' grades for several semesters and the average for all the grades ofthese students is 83. Her new class of 28 students seem to be higher than the average of ability and she wants to demonstrate that the current class is superior to the previous classes according to their average. Is there sufficient evidence for the class average of 86.2 and the standard deviation of 12 present to support her argument that the current class is superior? Using the 0.05 significance level.