j The seasonal output of a new experimental strain of pepper

j) The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 8.0 kilograms, and the standard deviation of the normally distributed weights is 2.0 kilograms. Of the 582 plants in the experiment, how many produced peppers weighing between 5.0 and 10.0 kilograms? (4)

A) 252

B) 475

C) 396

D) 504

E) None of the choices are correct

Solution

P( 5 < x < 10)

P( [5-8] / 2 < z < [10-8] / 2 )

P( -1.5 < z < 1) = 1-0.1587 - 0.0668 = 0.7745

0.7745 * 582 = 450.759

Of the 582 plants in the experiment, how many produced peppers weighing between 5.0 and 10.0 kilograms?

451 plants