omework: Section 7.3: Central Limit Theorem for Sample Prop core: 0 of 1 pt 3.37
ID: 3060141 • Letter: O
Question
omework: Section 7.3: Central Limit Theorem for Sample Prop core: 0 of 1 pt 3.37 Jures should have the same racial distritution as t e su Hw Score: 9.09%, 1 of 11 uring communites Abot 16% of residen sinaon an regon are a specific rac e. Suppose a local court randonly selects 50 ad totzens of the region to p in the jury pool. Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the proportion of available jurors of the above specific race is more than three standard errors from the population value of 0.16 s more than 10 times 50, n times p is 8, and n times (1 minus p) is 42, and both are more than Because the sampling distribution for the sample proportion is approximately nomal,it is known that the probability of faling within throe standard erors is about Therafore, e more than three standard errors away from the mean is about All parts showing 8 9 2 3 4 6 0Explanation / Answer
Correct Answer : 0.9973 , 0.00135
Explanation :
It is given that the distribution of sample proportion is approximately normal. For a normally distributed random variables, we know from the standard normal table, that probability of falling within three standard deviations is 0.9973. Hence correct answer in first blank is 0.9973.
Since, probability of falling withing 3 standard deviations is 0.9973; the probability of falling outside 3 standard deviations is 1- 0.9973 = 0.0027. Also, normal distribution is symmetric about its mean. Therefore, the probability of falling MORE (Right side tail) than 3 standard deviations away from mean is 0.5*0.0027 = 0.00135
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