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Calculating mean and standard deviation in the given case

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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.

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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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Solution describes the steps to calculate mean and standard deviation in the given case.

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Calculating mean and standard deviation in the given case..

A government agency has specialist who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted message. In standard English text, a particular letter is used at a rate of 5.9%

a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 1800 characters.

(Mean ?) = ________________
(Standard Deviation ?) = _____________

b. In an intercepted message, a page of 1800 characters is found to have the letter occurring 128 times. Is this unusual? Choose one below.

1. Yes, because 128 is below the minimum usual value.
2. Yes, because 128 is greater than the maximum usual value.
3. Yes, because 128 is within the range of usual values.
4. No, because 128 is within the range of usual values.

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