Question

A sample of 100 cans of peas showed an average weight of 14 ounces with a standard deviation of 0.7 ounces. If the distribution is fairly normal, how many cans will weigh over 14.7 ounces?

Answer 1

16

Explanation:

We are given that A sample of 100 cans of peas showed an average weight of 14 ounces with a standard deviation of 0.7 ounces.

So,
`\mu = 14`

`\sigma = 0.7`

Formula :
`z =(x-\mu)/(\sigma)`

Since we are supposed how many cans will weigh over 14.7 ounces

So, x = 14.7

`z =(14.7-14)/(0.7)`

`z =1`

So, Using z table

P(z>1)=1-P(z<1)=1-0.8413=0.1587

Since A sample contains 100 cans

So, No. of cans will weigh over 14.7 ounces =
`0.1587* 100`

=
`15.87`

So, no. of cans will weigh over 14.7 ounces is 16.

Answer 2

This is an example of a normal distribution. An average weight is 14 ounces and a standard deviation is 0.7 ounces.
14.7 = 14 + 0.7 = Average + 1 Standard Deviation.
It means that the percent of cans that will weigh over 14.7 ounces is:
100% - ( 50 % + 34 % ) = 100% - 84% = 16%
16% of 100 cans: 16/100 * 100 = 16.
Answer: 16 cans.