The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities.
2 answers:
You might be interested in
Answer:
The degrees of freedom are given by:
The p value for this case would be given by:
Step-by-step explanation:
Information given
represent the mean height for the sample
represent the sample standard deviation
sample size
represent the value that we want to test
t would represent the statistic
represent the p value for the test
Hypothesis to verify
We want to cehck if the true mean is lees than 25 mph, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic would be given by:
(1)
Replacing the info given we got:
The degrees of freedom are given by:
The p value for this case would be given by:
Answer:
DIRECT WAY EXCEL
"=NORM.DIST(75,80,3,TRUE)"
And we got:
OTHER WAY
And we can find this probability using the normal standard table or excel:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:
Where and
And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:
One way to do this in excel is with the following formula:
"=NORM.DIST(75,80,3,TRUE)"
And we got:
And the other way is use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel: