SOLUTION: Suppose certain coins have weights that are normally distributed with a mean of 5.078 g and a standard deviation of 0.072 g. A vending machine is configured to accept those coins w

Question 1152431: Suppose certain coins have weights that are normally distributed with a mean of 5.078 g and a standard deviation of 0.072 g. A vending machine is configured to accept those coins with weights between 4.948 g and 5.208 g.
a. If 270 different coins are inserted into the vending machine, what is the expected number of rejected coins?
The expected number of rejected coins is
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Probability coin is less than 4.948 grams:

z-score = = = -1.81

Look up -1.81 on a z-table. You get an answer of 0.0351. This is the probability the a coin is less than 4.948 grams.

Probability coin is more than 5.208 grams:

z-score = = = 1.81

Look up 1.81 on a z-table. You get an answer of 0.9649. This is the probability a coin is LESS than 5.208 grams. We want to find the probability a coin is MORE than 5.208 grams. So, if the probability a coin is less than 5.208 grams is 0.9649, the probability it is more than 5.208 grams is 0.0351.

So, the probability the coin does NOT fall in the accepted range is 0.0351 + 0.0351...or 0.0702.

Because there are 270 coins, and the probability a coin will be rejected is 0.0702, the number of expected rejected coins is:

270 * 0.0702 = 18.954...or, rounded off, 19.
RELATED QUESTIONS
Suppose certain coins have weights that are normally distributed with a mean of 5.661 g... (answered by Boreal)

suppose certain coins weights that are normally distributed with a mean of 5.285 g and a... (answered by Boreal)

Suppose certain coins have weights that are normally distributed with a means of 5.366 G... (answered by Boreal)

Suppose certain coins have weights that are normally distributed with a mean of 5.368 g... (answered by stanbon)

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a... (answered by Boreal)

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A... (answered by bosley5580)

The weight of 10000 items are normally distributed with a mean of 115kg and a standard... (answered by htmentor)

(1 point) The weights of unicorns are normally distributed. Suppose that a simple random... (answered by CPhill)

Question No. 9 The weights of a certain population of pregnant women are approximately... (answered by Boreal)