Question

The Crossett Trucking Company claims that the mean mass of its delivery trucks when they are fully loaded is 3000 kg and the standard deviation is 79 kg. Assume that the population follows the normal distribution. Forty trucks are randomly selected and their masses measured. Within what limits will 95% of the sample means occur? (Round the final answers to the nearest whole number.) Sample means

Answer 1

Solution :

Given that,

= 3000

= 79

n = 40

= 3000

= / n = 79 / 40

Using Empirical rule,

P(  - 2 < X <   + 2 ) = 95%

P(3000 - 2 * 79 / 40 < X < 3000 + 2 * 79 / 40 ) = 95%

P(3000 - 25 < X < 3000 - 25) = 95%

P(2975 < X < 3025) = 95%

2975 to 3025