A candy company claims that 10% of all their candy products are green. Suppose t
ID: 3293558 • Letter: A
Question
A candy company claims that 10% of all their candy products are green. Suppose that the candies are packaged at random in small bags containing about 200 candies. A class of elementary school students learning about percents opens several bags, counts the various colors of the candies, and calculates the proportion that are green. Complete parts a through c below. a) Explain why it's appropriate to use a Normal model to describe the distribution of the proportion of green candies they might expect. Select all that apply. A. The Success/Failure Condition is met since nq greaterthanorequalto 10. B. The Randomization Condition is met because the candies are randomly packaged into each bag. C. The Success/Failure Condition is met since np greaterthanorequalto 10. D. The 10% Condition is met because several bags of candy is far less than 10% of the population of candy. b) Use the 68-95-99.7 Rule to describe how this proportion might vary from bag to bag. About 68% will be between % and %, 95% will be between % and %, and 99.7% will be between % and %. (Use ascending order. Type integers or decimals rounded to one decimal place as needed.)Explanation / Answer
Part A
The Option A & C are correct.
Explanation:
since the expected number of green Candies is np = 200(0.10) = 20, which is greater than 10 and
nq = (200)(.9) = 180 therefore, the normal model applies to describe the distribution of proportion.
mean = .1
sd = sqrt(pq/n) = 0.021
b) 68% of the values lie within 1 standard deviation, so between 0.079 and 0.121
95% of the values lie within 2 sd, so between 0.058 and 0.142
99.7% of the values lie within 3 sd, so between 0.037 and 0.163
it would be very unusual for us to see values outside 3.7% and 16.3%.
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