In: Math

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 5,850 pounds and the standard deviation is 280 pounds. Assume that the population follows the normal distribution. Fifty trucks are randomly selected and weighed.

Within what limits will 95 percent of the sample means occur?

Solution :

Given that,

= 5850

= 280

n = 50

_{}
= 5850 and

_{}
=
/
n = 280 /
50 = 39.6

Using Empirical rule,

P(_{} -
2_{}
< X <
_{} +
2_{}
) = 95%

P(5850 - 2 * 39.6 < X < 5850 + 2 * 39.6) = 95%

P(5770.8 < X < 5929.2) = 95%

Limits are : 5770.8 and 5929.2

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