Question

3. For each situation, decide if it would be reasonable to use the normal distribution to describe the sampling distribution. Supply a brief explanation for each. (a) A polling company takes an SRS of 1000 voters and calculates the proportion who plan to vote in favor of Proposition 60. Previous polls suggest 26% are in favor of Prop. 60. (b) Brian rolls a fair 6-sided die 50 times and records the number of times “2” comes up.

Answer 1

A) Yes, it is reasonable to use the Normal Distribution as sampling distribution. This is so because the sample size, that is, 1000 is large enough to apply the Central Limit Theorem. Hence, we say that the sampling distribution is Normal here.

B) No, it is not reasonable to use the normal distribution. First off, the die is rolled only 50 times which is not a very big sample to be considered. Thereafter, 'number of times 2 comes up in the throw' is recorded which of course will be very less than 50. Hemce we do mot consider this as a large sample enough for CLT.