Probability and Statistics

Amanda123

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Jun 27, 2013
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Hello... There are two homework problems that I am having trouble with. I have no work to show because I don't know where to start let alone finish. Can someone who has time please look these over and show me step by step what they did to get the answer and what the answer is. Thank you so much :D

1. Research has found that 26% of all car seats are improperly installed. If the installation of 18 car seats is checked find the probability that : 1. exactly 5 of the seats will be installed incorrectly and 2. more than 10 of the seats will be installed incorrectly.

2. A local pub owner claims that his bar sells an average of 306 bottles of Corona beer a day. His "Silent" partner believes that the owner is overestimating this total. A random sample of 60 days, finds the average Corona sales to be 282 bottles a day with a standard deviation of 24 bottles. Based on this data and using a significance level of .05 is the partners claim true ?
 
Hello... There are two homework problems that I am having trouble with. I have no work to show because I don't know where to start let alone finish. Can someone who has time please look these over and show me step by step what they did to get the answer and what the answer is. Thank you so much :D

1. Research has found that 26% of all car seats are improperly installed. If the installation of 18 car seats is checked find the probability that : 1. exactly 5 of the seats will be installed incorrectly and 2. more than 10 of the seats will be installed incorrectly.

2. A local pub owner claims that his bar sells an average of 306 bottles of Corona beer a day. His "Silent" partner believes that the owner is overestimating this total. A random sample of 60 days, finds the average Corona sales to be 282 bottles a day with a standard deviation of 24 bottles. Based on this data and using a significance level of .05 is the partners claim true ?
We need to see your work to know where you are getting stuck. Please note that we are here to guide your work, not to give answers.

Hints to get started ..
1. Look up the binomial distribution.
2. Look up the sampling theorem.

Please show us now far you can get.
 
We need to see your work to know where you are getting stuck. Please note that we are here to guide your work, not to give answers.

Hints to get started ..
1. Look up the binomial distribution.
2. Look up the sampling theorem.

Please show us now far you can get.

Ok this is the first one... A. N =18, P= 0.26, X=5 = .2031 = 2%
B. N=18, P=0.26, X= 10 = .0011 = 11%
 
We need to see your work to know where you are getting stuck. Please note that we are here to guide your work, not to give answers.

Hints to get started ..
1. Look up the binomial distribution.
2. Look up the sampling theorem.

Please show us now far you can get.

For the second one I got 1.1402
 
Ok this is the first one... A. N =18, P= 0.26, P(X=5) = .2031 = 20.3%
B. N=18, P=0.26, X= 10 = .0011 = 0.11%
P(exactly 5) is correct, except you expressed the percentage wrong.

For the second part, P(more than 10), you have to do more work. In principal, you have to calculate
......P(>10) = P(11) + P(12) + P(13) + P(14) + P(15) + P(16) + P(17) + P(18)

The terms for large x become negligibly small. Start with x=11 and x=12, and continue till the terms are small enough that they don't affect the total any more.
......P(11) = p^11 (1-p)^7 18C11 = 0.00142
......P(12) = . . .
 
For the second one I got 1.1402
2. A local pub owner claims that his bar sells an average of 306 bottles of Corona beer a day. His "Silent" partner believes that the owner is overestimating this total. A random sample of 60 days, finds the average Corona sales to be 282 bottles a day with a standard deviation of 24 bottles. Based on this data and using a significance level of .05 is the partners claim true ?
More details please! I have no idea what the number "1.1402" represents. It can't be a probability or a confidence level, because it is >1. What does the sampling theorem tell you about the distribution of sample means, compared to the population? What is the probability that the average of N=60 samples from the assumed population distribution would be 282 or less?
 
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