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

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. 

Answer 2

Answer:

16

Step-by-step 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 : $z =\frac{x-\mu}{\sigma}$

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

So, x = 14.7

$z =\frac{14.7-14}{0.7}$

$z =1$

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 = $0.1587\times 100$

                                                                          = $15.87$

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