1. What percentage of the widget weights lie between 47 and 87 ounces? % c) What percentage of the widget weights lie above 55 ?

Question

question 1 details: The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 63 ounces and a standard deviation of 8 ounces.

question 2:

The time it takes me to wash the dishes is uniformly distributed between 6 minutes and 13 minutes.

What is the probability that washing dishes tonight will take me between 9 and 12 minutes?

Give your answer accurate to two decimal places.

question 3:

The probability density of a random variable X is given in the figure below.

From this density, the probability that X is between 0.56 and 1.9 is

question 4:

The probability density of a random variable X is given in the figure below.

From this density, the probability that X is at least 0.12 is

question 5:

The probability density of a random variable X is given in the figure below.

From this density, the probability that X > 1.1 or X < 0.26 is:

Answer 1

1 87-63 = 24 24/8 = 3 standard deviations above the mean

63 -47 = 16 16/8 = 2 standard deviations below the mean

use the empirical rule 68-95-99.7% for 1, 2 and 3 standard deviations from the mean

99.7/2 = 49.85% above the mean

95/2 = 47.5% below the mean

49.85+47.5 = 97.35% between 63 and 87

2 (12-9)/(13-6) = 3/7 = about 42.86% probability between 9 and 12 minutes

3 (1.9-.56)/2 = 1.35/2 = 0.675 = 67.75% probability

4 (2-.12)/2 = 1.88/2= 0.94 = 94%

5 (.26+2 -1.1)/2 = 1.16/2 = .58 = 58%