# Stat 202: Lecture 15 (covers pp. 171-187)

Nathan VanHoudnos
10/31/2014

### Agenda

2. Lecture 16 (covers pp. 171-187)

### Checkpoint #17

What is the average percentage correct for this activity?

• 60% correct

### Question 1 Checkpoint #17

Which of the following statements about the sampling distribution of the sample mean, x-bar, is not true?

• a) The distribution is normal regardless of the shape of the population distribution, as long as the sample size $$n$$ is large enough.
• b) The distribution is normal regardless of the sample size, as long as the population distribution is normal.
• c) The distribution's mean is the same as the population mean.
• d) The distribution's standard deviation is smaller than the population standard deviation.
• e) All of the above statements are correct.

### Question 4 Checkpoint #17

Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean $$\mu = 50$$ grams and standard deviation $$\sigma = 2$$ grams.

If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?

• a) There is no way to evaluate this likelihood, since the sample size (n = 4) is too small.
• b-d) There is about a __ chance of this occurring.
• e) It is extremely unlikely for this to occur; the probability is very close to 0.