Question

Please explain this.

A chocolate candy maker sells chocolates in bags. The company performs tests to find out how consistent the number of candies per bag is. After analysis, they find that the data is normally distributed with an average of 36 candies per bag and a standard deviation of 3 candies.

Which of the following statements is/are justified based on the data?

There may be more than one correct answer. Select all that apply.

A. Approximately 99.7% of the bags have between 27 and 45 candies.

B. Approximately 95% of the bags have between 30 and 42 candies.

C. Approximately 68% of the bags have between 35 and 37 candies.

D. Approximately 68% of the bags have between 33 and 39 candies.

E. Approximately 99.7% of the bags have between 28 and 44 candies.

F. Approximately 95% of the bags have between 27 and 45 candies.

Answer 1

The data is normally distributed so as per the empirical rule,

Approx 68% bags will lie between 1 standard deviation from the mean i.e. between (36 - 3) and (36 + 3) candies i.e. between 33 and 39 candies.

Approx 95% bags will lie between 1 standard deviation from the mean i.e. between (36 - 2*3) and (36 + 2*3) candies i.e. between 30 and 42 candies.

Approx 99.7% bags will lie between 1 standard deviation from the mean i.e. between (36 - 3*3) and (36 + 3*3) candies i.e. between 27 and 45 candies.

Options A, B and D are correct.