The Empirical Rule The following data represent the weights (in grams) of a random sample of 50 M&M plain candies.

(a) Determine the sample standard deviation weight. Express your answer rounded to three decimal places.

(b) On the basis of the histogram drawn in Section 3.1, Problem 27, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of M&Ms.

(c) Use the Empirical Rule to determine the percentage of M&Ms with weights between 0.803 and 0.947 gram.

(d) Determine the actual percentage of M&Ms that weigh between 0.803 and 0.947 gram, inclusive.

(e) Use the Empirical Rule to determine the percentage of M&Ms with weights more than 0.911 gram.

(f) Determine the actual percentage of M&Ms that weigh more than 0.911 gram.

Answer :

Step 1

a)

First we need to find mean.

=

=

= 0.766

Here standard deviation is

=

= 0.0012

Then the sample variance is

s=

s =

s = 0.036

Hence the sample variance is s = 0.036 gram.

b)

The histogram is given below.

The histogram is approximately symmetric, so the Empirical Rule is applicable.

c)

95% of the M&Ms should weigh between 0.803 and 0.947 gram.

d)

96% of the M&Ms actually weigh between 0.803 and 0.947 gram.

e)

16% of the M&Ms should weigh more than 0.911 gram.

f)

12% of the M&Ms actually weigh more than 0.911 gram.

Problem