## The distribution of actual weight of tomato soup in a 16 ounce can is thought to be be shaped with a ean equal to 16 ounces, and a standard

Question

The distribution of actual weight of tomato soup in a 16 ounce can is thought to be be shaped with a ean equal to 16 ounces, and a standard deviation equal to 0.25 ounces. Based on this information, between what two values could we expect 95% of all cans to weigh?

(a) 15.75 to 16.25 ounces

(b) 15.50 to 16.50 ounces

(c) 15.25 to 16.75 ounces

(d) 15 to 17 ounces

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1 month 2021-10-18T15:41:55+00:00 1 Answer 0 views 0

(b) 15.50 to 16.50 ounces

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 16

Standard deviation = 0.25

Based on this information, between what two values could we expect 95% of all cans to weigh?

By the Empirical Rule, within 2 standard deviations of the mean. So

16 – 2*0.25 = 15.50 ounces

16 + 2*0.25 = 16.50 ounces