Question

The foreman of a bottling plant has observed that the amount of soda in each 30-ounce...

The foreman of a bottling plant has observed that the amount of soda in each 30-ounce bottle is actually a normally distributed random variable, with a mean of 30.3 ounces and a standard deviation of 0.28 ounce. If a customer buys a carton of six bottles, what is the probability that the mean amount of the six bottles will be greater than 30 ounces? a. 0.9956 b. 0.8577 c. 0.1423 d. 0.0044

Homework Answers

Answer #1

Given,

= 30.3

= 0.28

If a customer buys a carton of six bottle

i.e n = 6

Noe calculate p(x > 30)

p(x> 30) = 0.5 + p(0 < z < x-/(/n))

= 0.5 + p(0 < z < 30-30.3/(0.28/6))

= 0.5 + p(0 < z < -2.62)

= 0.5 + 0.4956

p(x > 30) = 0.9956

Hence option (a) is correct.

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
The foreman of a bottling plant has observed that the amount of soda in each 30-ounce...
The foreman of a bottling plant has observed that the amount of soda in each 30-ounce bottle is actually a normally distributed random variable, with a mean of 30.3 ounces and a standard deviation of 0.28 ounce. If a customer buys a carton of six bottles, what is the probability that the mean amount of the six bottles will be greater than 30 ounces? Select one: A. 0.8577 B. 0.1423 C. 0.0044 D. 0.9956
A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and...
A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with an amount more than 20.3 ounces or are you more likely to select a sample of eight bottles with a mean amount more than 20.3 ounces? Explain.
A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and...
A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with more than 21.3 ounces or are you more likely to select a sample of eight bottles with a mean amount of more than 21.3 ounces? Explain.
The amount of soda in a 16-ounce can is normally distributed with a mean of 16...
The amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of .5 ounce. What is the probability that a randomly selected can will have greater than 15 ounces and less than 16.5 ounces? Round your answers to four decimal places. .1587 .9772 .8185 .8413 .9500
The Crown Bottling Company has just installed a new bottling process that will fill 20-ounce bottles...
The Crown Bottling Company has just installed a new bottling process that will fill 20-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, µ, is close to the target fill of 20 ounces. To this end, a random sample...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample...
A bottling machine can be regulated so that it discharges an average of ounces per bottle....
A bottling machine can be regulated so that it discharges an average of ounces per bottle. It has been observed that the amount of fill (Y) dispensed by the machine is normally distributed with sigma = 1 ounce. If Y1, Y2, ..., Y16 is a random sample from the output of the machine on a given day (all bottled with the same machine setting). (a) What is the mean of barY? i.e. µ = ? (b) What is the standard...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample...
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer . It...
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer . It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.14 ounces and a standard deviation of 0.06 ounce. a)Find the probability that the bottle contains fewer than 12.00 ounces of beer.Label the sketch of the normal curve with the values from the problem situation. Label the mean and the desired outcome. Use a...
In a plant that fills 12 ounce cans of soda, the mean fill amount with the...
In a plant that fills 12 ounce cans of soda, the mean fill amount with the current machinery is 12.2 ounces with a standard deviation of 0.03 ounces. A new machine is said to be more accurate, so the company tested this new machine on a run of 10 cans, and obtained the following fill amounts: 12.03 12.10 12.02 11.92 12.10 12.00 12.05 11.97 11.99 11.87 Test the claim that the standard deviation of the new machine is lower than...