Question

Part 1 of 3

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8591 g and a standard deviation of 0.0513 g. A sample of these candies came from a package containing 461 ​candies, and the package label stated that the net weight is 393.5 g.​ (If every package has 461 ​candies, the mean weight of the candies must exceed
393.5
461=0.8535 g for the net contents to weigh at least 393.5 ​g.)
a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8535 g.
The probability is
​(Round to four decimal places as​ needed.)

Answer 1

we need to calculate a z-score and refer to the normal distribution tables.

Remember that not all distribution tables read the same way, but they should show you by a diagram whether the percentage given is for the area to the left of the z or to the right.

Z = (X - μ)/σ or Z = (.8543 - .8605)/.0513 = -.1209

The area to the right of this Z-score translates to a probability of 0.5478