Question

Suppose certain coins have weights that are normally distributed with a mean of 5.159 g and...

Suppose certain coins have weights that are normally distributed with a mean of 5.159 g and a standard deviation of 0.079 g. A vending machine is configured to accept those coins with weights between 5.029 g and 5.289 g. If 270 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.029 g and 5.289 g?

Homework Answers

Answer #1

Solution : Given that mean ? = 5.159 and a standard deviation ? = 0.079

=> P(5.029 < x < 5.289) = P((x - ?)/? < Z < (x - ?)/?)
  
= P((5.029 - 5.159)/0.079 < Z < (5.289 - 5.159)/0.079)
  
= P(-1.6456 < Z < 1.6456)

= 0.901

=> Given n = 270
  
=> P(5.029 < x < 5.289) = P((x - ?)/(?/sqrt(n)) < Z < (x - ?)/(?/sqrt(n)))
  
= P((5.029 - 5.159)/(0.079/sqrt(270)) < Z < (5.289 - 5.159)/(0.079/sqrt(270))
  
= P(-27.0395 < Z < 27.0395)

= 1

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose certain coins have weights that are normally distributed with a mean of 5.271 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.271 g and a standard deviation of 0.079 g. A vending machine is configured to accept those coins with weights between 5.181 g and 5.361 g. a. If 300 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins? The expected number of rejected coins is __________. ​(Round to the nearest​ integer.) b. If 300 different coins are inserted into the...
Suppose certain coins have weights that are normally distributed with a mean of 5.854 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.854 g and a standard deviation of 0.071 g. A vending machine is configured to accept those coins with weights between 5.744 g and 5.964 g. a. If 280 different coins are inserted into the vending machine, what is the expected number of rejected coins?
Suppose certain coins have weights that are normally distributed with a mean of 5.938 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.938 g and a standard deviation of 0.078 g. A vending machine is configured to accept those coins with weights between 5.848 g and 6.028 g. If 260 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?
Suppose certain coins have weights that are normally distributed with a mean of 5.629 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.629 g and a standard deviation of 0.056 g. A vending machine is configured to accept those coins with weights between 5.559 g and 5.699 g. a. If 280 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?
suppose certain coins have weights that are normally distributed with a mean of 5.191g and a...
suppose certain coins have weights that are normally distributed with a mean of 5.191g and a standard deviation of 0.068 g. A vending machine is configured to accept those coins with weights between 5.121 g and 5.261 g. If 260 different coins are inserted into the vending machine, what is the expected number rejected coins.
Suppose certain coins have weights that are normally distributed with a mean of 5.395 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.395 g and a standard deviation of 0.058g.A vending machine is configured to accept those coins with weights between 5.325g and 5.465 g If 290 different coins are inserted into the vending machine ,what is the expected number of rejected coins?! The expected number of rejected coins is...(round to nearest integer)
Suppose certain coins have weights that are normally distributed with a mean of 5.517 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.517 g and a standard deviation of 0.055 g. A vending machine is configured to accept those coins with weights between 5.427 g and 5.607 g a. If 260 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins? The expected number of rejected coins is? ​(Round to the nearest​ integer.)
Suppose certain coins have weights that are normally distributed with a mean of 5.414 g and...
Suppose certain coins have weights that are normally distributed with a mean of 5.414 g and a standard deviation of 0.069 g. A vending machine is configured to accept those coins with weights between 5.294 g and 5.534 g. a. If 280 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins? The expected number of rejected coins is ---Round to the nearest integer
6. Assume that the weights of coins are normally distributed with a mean of 5.67 g...
6. Assume that the weights of coins are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected by the machine? Give your answer in the percentage format (using % symbol), rounded to two decimal places. 7. Assume that values of variable x are normally distributed, with the mean μ = 16.2 and the...
3. Weights of quarters are normally distributed with a mean of 5.67 g and a standard...
3. Weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If many counterfeit coins are found, you can narrow the range of acceptable weights with the effect that most counterfeit coins are rejected along with some legitimate quarters. 3. a)  If you adjust your vending machines to accept weights between 5.60 g and 5.74...