Deciding whether the normal distribution applies: 6. For each situation, circle

Question

Deciding whether the normal distribution applies: 6. For each situation, circle "yes" if it would be reasonable to use the normal distribution, or no" if it would not be. Supply a brief explanation for each (a) A polling company takes a 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. (Yes I No) (b) Brian rolls a fair 10-sided die 50 times and records the number of times "O" comes up (most 10-sided dice are labeled 0-9, not 1-10). (Yes I No) measures their height, to calculate the average height. (Yes I No) vote in favor of Proposition 881 . Previous polls suggest 4% are in favor of Prop, 881 . (Yes I No) measures their height, to calculate the average height. (Yes I No) (c) A clothing store randomly selects 20 customers, and, after getting their permission, (d) A polling company takes a SRS of 200 voters and calculates the proportion who plan to (e) A clothing store randomly selects 60 customers, and, after getting their permission, (0 Brian rolls a fair 10-sided die 500 times and records the number of times "8" comes up (Yes I No)

Explanation / Answer

6. (a) Since, the sample size is greater than 30, np = 260 > 10, n(1-p) = 740 > 10, we can apply Normal distribution. So the answer is Yes.

(b) Here, np = 50 * 0.1 = 5 < 10, so Normal distribution is not applicable. So the answer is No.

(c) Here sample size is less than 30, so Normal distribution is not applicable. So the answer is No.

(d) Here, np = 200 * 0.04 = 8 < 10. So, we can't apply Normal distribution. So the answer is No.

(e) Here the sample size is greater than 30, so we can apply Normal distribution. So the answer is Yes.

(f) Here, n > 30, np = 500 * 0.1 = 50 > 10, n(1 - p) = 500 " 0.9 = 450 > 10. So, we can apply Normal distribution. So, the answer is Yes.

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