Statistics and Probability Answers

Consider all sample of size 3 from this population: 67,80,70,78,70,73,67,71,88 and 90

Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6 , 7 and 8. Construct the sampling distribution of the sample means and determine its standard deviation.

The weights of the Grade 11 students are known to be normally distributed with a mean of 54 kg and a standard deviation of 8 kg. Find the percentage of Grade 11 students with weights between 45 kg and 66 kg.

The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 2.5 work-related injuries a month. What is the probability that in a given month, no work-related injuries occur? That at least one work-related injury occurs?

• Population consists of these three numbers 1 2 3 and 4 list all the possible samples of size n = 2 which can be drawn with replacement from the population.

According to one of the teachers in your school, the senior high school students sleep for 7 hours a day on a weekday. You wanted to prove this claim by making a survey of 50 senior high school students. You will be asking the students about how long they sleep in a regular weekday. Record the results of your survey. As a researcher, you need to compute the mean and standard deviation of your sample.

Create a 90%, 95%, and 99% confidence interval for the mean time of sleep for senior high school students. In your report, the raw data should be present, and the computation should be complete

A machine produces cylindrical metal pieces. A sample of pieces is taken, and the diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01 and 1.03 cm. Find the t-value for a 98% confidence interval for the diameters of the cylindrical metal pieces. Assume that the diameters are approximately normally distributed.