Question

1. Raul received a score of 80 on a history test, the z-score is 1.34. He received a score of 85 on a biology test, the z-score is 1.30. On which test did he do better relative to the rest of the class?

a. History test b. Biology test c. He scored the class average on both the History and Biology test.

2. Which probability, P(z < -1.18) or P(z > 1.18) is greater? a. P(z < -1.18) b. P(z > 1.18) c. The probabilities are the same

3.) According to the Central Limit Theorem, as the sample size decreases, the standard deviation of the sampling distribution _____________. a. Decreases b. Increases c. Stays the same

4.) If z = 0, which of the following must be true? a. Corresponding x-value is zero b. Corresponding x-value is equal to the population mean c. Population mean is zero

Answer 1

Q1) The score on history test has a z score of 1.34, which means that the score on history test is 1.34 standard deviations greater than the mean history test score while for the biology test, the as the z score is 1.3, it is only 1.3 standard deviation greater than the mean biology test score. Therefore Raul did better on the history test than on the biology test.

Q2) The probabilities here are computed as:
P(Z < -1.18) or P(Z > 1.18)

Note that as normal distributions are symmetric about 0,
Therefore, P(Z < -c) = P(Z > c) for any real number c.

Therefore both the probabilities are same here.

Q3) The standard deviation of the sampling distribution of sample mean is computed as:

As the sample size decreases, clearly the standard error here would increase. Therefore Increases is the correct answer here

Q4) For Z = 0, the value X is equal to the mean of the distribution. Therefore the corresponding x-value here is equal to the population mean.