Calculating mean and standard deviation in the given case

A candy company claims that 17% 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.

b. A random sample of 100 candies contains 5 orange candies. Is this result unusual? Does it seem that the claimed rate of 17% is wrong? Choose one from below

1. Yes, because 5 is below the minimum usual value. Thus, the claimed rate of 17% is probably wrong.
2. Yes, because 5 is greater than the maximum usual value. Thus, the claimed rate of 17% is not necessarily wrong.
3. Yes, because 5 is within the range of usual values. Thus, the claimed rate of 17% is probably wrong.
4. No, because 5 is within the range of usual values. Thus, the claimed rate of 17% is not necessarily wrong.

Solution Preview

a. Find the mean and standard deviation for the number of orange candies in such groups of 100.
Number of observations=n=100
Probability of being orange=p=17%=0.17
q=1-p=1-0.17=0.83

Mean=np=100*.17=17
Standard deviation=npq=100*0.17*0.83=14.11

b. A ...

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