Question

The weights of a certain brand of candies are normally distributed with a mean weight of

0.85860.8586

g and a standard deviation of

0.05170.0517

g. A sample of these candies came from a package containing

464464

​candies, and the package label stated that the net weight is

396.0396.0

g.​ (If every package has

464464

​candies, the mean weight of the candies must exceed

StartFraction 396.0 Over 464 EndFraction396.0464equals=0.85340.8534

g for the net contents to weigh at least

396.0396.0

​g.)

a. If 1 candy is randomly​ selected, find the probability that it weighs more than

0.8534

g.

Answer 1

Given:

Mean, = 0.8586

Standard deviation, = 0.0517

Sample size , n = 464

To find :

If 1 candy is randomly​ selected, the probability that it weighs more than 0.8534

Let X : The weights of a certain brand of candies.

X follows Normal distribution with = 0.8586 and = 0.0517.

Now,

If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8534 is

P( > 0.8534)

= P( - //√n > P(0.8534 - 0.8586/0.0517/√464

= P(z > -2.17)

= 1 - P(z < -2.17)

= 1 - 0.0150...... ( from z table)

= 0.9850

Therefore the probability that it weighs more than 0.8534 is 0.9850