Question

Can some one help me with this probability
A can of pepsi is supposed to contain, on the average 12 ounces of soda with a standard deviation of .3 ounces.Suspecting fraud, you take a random sample of 40 cans and measure the amount of pepsi in each. Your measurements show that the 40 cans had mean of 11.9 ounces. What is the probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less?

Answer 1

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Answer 2

First of all use the standard score formula:
\[z-score=\frac{ StandardMea-StandardValue }{ Standard Deviation }\]
\[z-score=\frac{ 11.9-12 }{ 0.3 }=-0.3(3)\]
Now that the z-score is known calculate the probability:
\[P(z<-0.3(3))=1-P(z<0.3(3))=1-0.6293=You do the math\]

Answer 3

The sample is large enough (>30) for the Central Limit Theorem to hold.
First standardize x bar:
\[Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{11.9-12}{\frac{0.3}{\sqrt{40}}}=-2.11\]
The problem now reduces to finding the cumulative probability for a z-score of -2.11 using a standard normal distribution table:
\[P(Z<-2.11)=0.0174\]

Answer 4

two different problem two different answers.

Answer 5

@kropot72 can you check this for mea coin is unbalanced such that it comes up tails 55 of the time in an effort to prove that the coin is unfair an experiment flips the coin 50 times

a) =BINOM.DIST(25,50,0.55,TRUE) 1-.284 = .716 --> 71.6%

b) =BINOM.DIST(30,50,0.55,TRUE) --> 1-.803 = .197 --> so only a 19.7%

c) =BINOM.DIST(25,50,0.55,FALSE) --> 8.73%

Answer 6

@ganeshie8 can you review this for me

Answer 7

0.0174 is correct for ur first problem

Answer 8

The questions for the A) B) and C)

A) What is the probability that the coin comes up tails more that 25 times

B)What is the probability that the coin comes up tails more than 30 times?

C) what is the probability that the coin comes up tails exactly 25 times?

Answer 9

not sure about the binom distribution problem sorry :(

Answer 10

you may use this to verify :

http://stattrek.com/online-calculator/binomial.aspx

Answer 11

okay will do

Answer 12

According to that site,

71.6% is correct for part A

Answer 13

19.7% is also correct for part B

Answer 14

8.73% is correct for part B

Answer 15

Okay thanks for the for the website, and your help :)

Answer 16

np :)