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 normal, how many cans of peas will fall between 12.6 and 15.4 ounces?

Answer 1

Answer:

96 cans

Step-by-step explanation:

Mean = $\mu = 14$

Standard deviation = $\sigma = 0.7$

n = sample size = 100 cans

Now to find how many cans of peas will fall between 12.6 and 15.4 ounces:

Formula: $z=\frac{x-\mu}{\sigma}$

At x = 12.6

$z=\frac{12.6-14}{0.7}$

$z=-2$

At x = 15.4

$z=\frac{15.4-14}{0.7}$

$z=2$

Now to find P(12.6<z<15.4)

Using z table

P(-2<z<2)=P(z<2)-P(z<-2)=0.9772-0.0228=0.9544

Number of cans between 12.6 and 15.4 ounces= $0.9544 \times 100$

                                                                              = $95.44$

Thus 96 cans fall between 12.6 and 15.4 ounces.

Answer 2

12.6 to 15.4 divided by 0.7 is -2 to +2 by the empirical rule 95% of the cans will be within 2 standard deviation of the weight 95