Question

Homework: Section 7.3: Central Limit Theorem for Sample Prop Hw Score: 27.27%, 3 of 11 7 of 11 (5 Score: 0 of 1 pt Question Help 7.3.41 aken in such a way that the conditions for using the Centrail Limit Theorem are met. We are interested in finding the probability that the proportion of overweightobese children in the sample will be greater than 0.54 XA The answer should be less than 50%, because the resulting z-soore will be negative and the sampling distribution is approximately B. The answer should be ess than 50%, because 054 is less tan the The vswer shuld be geaar tan 50% because the resulting z score wil be po tree and he samping darbuonoomseyens C. ★D The answer should be geater than 50%, because 0 54 is less than the population proportion of 0.58 and because the sampling distribution is agproximately Normal. b Calculate the probabity墬at 54% or more ofthe sample are overweight or obeso P(p2054).□Rund to tree decinal places as needed.) 2 3 4 5 6 8 9 0

Answer 1

a. As 0.54 lies left to 0.58 (mean of the sampling distribtution), Probability that proportion greater than 0.54 is greater than 50% (area to the right of 0.54 is greater tha 50% as area to the right of 0.58 is 50%)

b. P(p>= 0.54)

$= P(Z>\frac{0.54-0.58}{\sqrt{\frac{0.58(1-0.58)}{200}}}) = P(Z>-1.1461) = 0.8741$

= 0.874 rounded)