Statistics and Probability Answers

Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.

The weight (in kg) of grade 11 students in section Z follows a normal distribution with a mean 48 and a standard deviation of . Find the probability that students choosen at random has a weight less than 45

In a shipment of 10 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested?

The quality of the drinking water must be monitored as often as possible. One variable of concern is

the pH level, which measures the alkalinity or acidity of the water. A pH below 7.0 is acidic while a pH

above 7.0 is alkaline. A pH of 7.0 is neutral. A water-treatment plant is targeting higher than 8.0 pH. Based

on 16 random water samples, the mean and standard deviation were found to be: 𝑋 ̅=7.6 and s = 0.4. Test

the claim using 5%

Step

1 Describe the population parameter of interest

2 Formulate the null and alternative hypothesis

3 Check the assumptions

4 Choose a signifinance level size for α

5 Select the appropriate test statistic

Compute the test statistic using the appropriate formula

6 State the decision rule for rejecting or not the null hypothesis

7 Compare the computed test statistic and the critical value /s

1. Given the population 2,4,6 and 8. Suppose samples of size 3 are drawn from this population.

a. Determine the number of possible samples of size n that can be drawn from a given population of size n.

A group of 8 students in your class having the weight of 50, 52, 53, 54, 56, 57, 58, and 60.

1.Calculate the standard deviation of the sampling distribution of the sample means. Compare this to the standard deviation of the population. 

A tree if less than three feet high and when transplanted has a 40% chance of survival. If six such trees are transplanted, what is the probability that at most four five will not survive?

A job placement director claims that the average starting salary for nurses is P12,000. A sample of 10 nurses has a mean of P11,750 and a standard deviation of 200. Is there enough evidence to reject the director’s claim at alpha = 0.05

A job placement director claims that the average starting salary for nurses is P12,000. A sample of 10 nurses has a mean of P11,750 and a standard deviation of 200. Is there enough evidence to reject the director’s claim at alpha = 0.05

EA Sports have asked you (an analyst) to find out the mean and standard deviation of the number of minutes people take to complete level 1 of their new game using the below information: The number of minutes people spend playing level 1 follows a normal distribution The probability of player playing for less than 5 minutes is 0.0045 The probability of someone taking less than 15 minutes to complete level 1 is 0.9641