Question

The following data represent the weights (in grams) of a random sample of 50 candies. 0.82 0.81 0.91 0.95 0.74 0.89 0.87 0.75 0.81 0.95 0.88 0.78 0.76 0.75 0.71 0.84 0.87 0.91 0.75 0.75 0.85 0.96 0.85 0.81 0.83 0.88 0.83 0.94 0.76 0.83 0.97 0.71 0.85 0.81 0.85 0.81 0.83 0.86 0.86 0.91 0.82 0.71 0.83 0.86 0.92 0.82 0.82 0.78 0.77 0.81 (a) Determine the sample standard deviation weight. s= 0.07 gram (Round to two decimal places as needed.) 20 (b) On the basis of the histogram on the right, comment on the appropriateness of using the empirical rule to make any general statements about the weights of the candies. The histogram is not bell-shaped so the empirical rule cannot be used. The histogram is bell-shaped so the empirical rule can be used. 07 0.7 (c) Use the Empirical Rule to determine the percentage of candies with weights between 0.69 and 0.97 gram. Hint: x=0.83 %

Answer 1

Assuming that the above findings are true, let X be the random variable denoting the weight of the candies.

According to the estimates,

X ~ N(0.83, 0.074)

We are to find:

$=P(X<0.97)-P(X<0.69)$
$=P(\frac{X-0.83}{0.07}<\frac{0.97-0.83}{0.07})-P(\frac{X-0.83}{0.07}<\frac{0.69-0.83}{0.07})$

= P(Z < 2) - P(Z <-2)

$=\Phi(2)-\Phi(-2)$
$=0.97724987-0.02275013$
$=0.95449974$
$=0.9545$

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