Question

1. A​ fruit-packing company produced peaches last summer whose weights were normally distributed with mean 15 ounces and standard deviation 0.6 ounce. Among a sample of 1000 of those​ peaches, about how many could be expected to have weights of more than 13 ​ounces?

The number of peaches expected to have weights of more than 13 ounces is

2. A​ fruit-packing company produced peaches last summer whose weights were normally distributed with mean 16

ounces and standard deviation 0.6 ounce. Among a sample of 1000 of those​ peaches, about how many could be expected to have weights between 15.5 and 17.5 ​ounces?

The number of peaches expected to have weights between 15.5 and 17.5 ounces is

Answer 1

Solution :

Given that ,

1) mean = = 15

standard deviation = =0.6

n = 1000

P(x > 13) = 1 - p( x< 13)

=1- p P[(x - ) / < (13 - 15) / 0.6]

=1- P(z < -3.33)

Using z table,

= 1 - 0.0004

= 0.9996

= 1000 * 0.9996 = 999.6

= 1000

2) mean = = 16

standard deviation = = 0.6

n = 1000

P(15.5 < x < 17.5) = P[(15.5 - 16) / 0.6) < (x - ) /  < (17.5 - 16) / 0.6) ]

= P(-0.83 < z < 2.5)

= P(z < 2.5) - P(z < -0.83)

Using z table,

= 0.9938 - 0.2033

= 0.7905

= 1000 * 0.7905 = 790.5

= 791