Statistics and Probability Answers

Activity 2. Construct Me!

A population consists of the five numbers 2, 3, 6, 8 and 11.

Consider samples of size 2 that can be drawn from this population.

a. List all the possible samples and the corresponding mean.

Sample

Mean

19

b. Construct the sampling distribution of the sample means.

Sample Mean

Probability

Frequency

c. Draw a histogram of the sampling distribution of the

meets.

According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? [10] (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? [10]

The Head of the Math Department announced that the mean score of Grade 11 students in St. James High School in the medterm examination in statistics and probability was 88 and the standard deviation was 10. One student who believed that the mean score was less than this, randomly selected 35 students and computed their mean score. She obtained a mean score of 84. At 0.01 level of significance, test the student’s belief.

If scores are normally distributed with the mean of 30 and standard deviation of 5. what percent score is.

given the population mean of 12 and a sample deviation of 3 in a sample size of 125

A producer of new corn seed guarantees that 85% of the seeds will germinate. A gardener plants 10 of the seeds. What is the probability that;

a) None will grow

b) Six will grow

c) At least nine will grow

Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63.

Determine the standard error of the sample means

Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63.

Find the mean of the mean of the sample means

The Head of the Math Department announced that the mean score of Grade 11 students in St. James High School in the medterm examination in statistics and probability was 88 and the standard deviation was 10. One student who believed that the mean score was less than this, randomly selected 35 students and computed their mean score. She obtained a mean score of 84. At 0.01 level of significance, test the student’s belief.

Random samples with size 5 are drawn from the population containing the values 26, 32, 41, 50, 58, and 63.

Construct the distribution of the mean of all samples.