Answer to Question #277829 in Statistics and Probability for Amy

Question

 1.    The net amount of jam in a standard jar produced by a certain food manufacturer has a normal distribution with mean 340 grams and standard deviation 5 grams.

a.    A jar of jam is rejected if its amount differs from the mean by more than 6 grams.

 

What is the probability that a randomly selected jar of jam will be rejected?

 

[4 marks]

 

b.    Estimate the number of rejected jars if a wholesaler has ordered 500 jars of jam from the manufacturer.

 

c.     Estimate the number of accepted jars if a wholesaler has ordered 300 jars of jam from the manufacturer.

Answer 1

a.

$z=\frac{x-\mu}{\sigma}=\pm\frac{6}{5}=\pm 1.2$

probability that a randomly selected jar of jam will be rejected:

$P(z<-1.2)+P(z>1.2)=2\cdot0.1151=0.2302$

b.

number of rejected jars:

$500\cdot0.2302=115.1\approx115$

c.

number of accepted jars:

$300(1-0.2302)=230.94\approx231$