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100

Find the z-value of 1.01. 

0.8438

100

Find the z-value of 3.47. 

0.9997

100

Find the z-value of 2.05. 

0.9798

200

Find the mean of 8, 9, 10. 

9

200

Find the mean of 10.12, 15.9, 12.56, and 23.68.

15.565

200
Find the mean of 29.165, 39.788, 17.249, and 75.638.

40.46

300

Mrs. Dela Cruz gave a 50-item test to her 115 Grade 12 students. The result of the exam shows an average score of 36 with a standard deviation of 2.7. Suppose Mrs. Dela Cruz repeatedly took 33 samples and calculated the sample mean from each sample.

a. Find the mean of the sample means.

b. Compute for the standard error of the sample mean.

c. Determine the shape of the sampling distribution of the sample mean.

Therefore, the mean of the sample means is μx̅ = 36 with standard error σx̅ ≈ 0. 3986. Moreover, the sampling distribution of the sample mean is approximately bell- shaped.

300

Given a population that consists of 110, 120, 130, 140, and 150. Using a sample size of 2 without replacement, illustrate the Central Limit Theorem through the mean and standard deviation of the sampling distribution of the sample mean.

Since we arrive at σX = 8.66, the relationship holds

true.

300

Sheldon owns a mango farm and the weight of his mangoes are normally distributed with an average weight of 200 grams and a standard deviation of 15 grams. If there are 800 mangoes in the farm, what is the mean and standard deviation of the sample mean weights of 50 mangoes?

Therefore, μx̅ = 200 grams and σx̅ ≈ 2. 06 grams.