A candy company claims that 16% of its plain candies are orange, and a sample of
ID: 3045094 • Letter: A
Question
A candy company claims that 16% of its plain candies are orange, and a sample of 100 such candies is randomly selected. a. Find the mean and standard deviation for the number of orange candies in such groups of 100 = 16 = 3.7 Round to one decimal place as needed b. A random sample of 100 candies contains 5 orange candies. Is this result unusual? Does it seem that the claimed rate of 16% is wrong? .) A. B. ° C. D. Yes, because 5 is greater than the maximum usual value. Thus, the claimed rate of 16% is probably wrong Yes, because 5 is within the range of usual values Thus, the claimed rate of 16% is probably wrong No, because 5 is within the range of usual values Thus, the claimed rate of 16% is not necessarily wrong Yes, because 5 is below the minimum usual value. Thus, the claimed rate of 16% is probably wrongExplanation / Answer
Given : p = 0.16 n = 100
a. Mean = n * p
= 100 * 0.16 = 16.
= (np(1-p))
= (16 * (1 - 0.16))
= (16 * 0.84)
= 13.44
= 3.6661.
b. Since the sample contains 5 orange out of 100 candies, the proportion is 5/100 = 5% which is way below the claimed 16%.
D. Yes, because 5 is below the minimum usual value. Thus the claimed rate of 16% is probably wrong.
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