Answer:
a)
And we can find this probability using the normal standard table or excel:
b)
And we can find this probability using the complement rule and the normal standard table or excel:
c)
And we can find this probability with this difference:
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 life of a particular brand of a population, and for this case we know the distribution for X is given by:
Where and
Part a
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score 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:
Part b
And we can find this probability using the complement rule and the normal standard table or excel:
Part c
For this case we select a sample size of n =16. and we want this probability:
We know that the distribution for the sample mean is given by:
And we can find the z scores for the limits like this:
And we can find this probability with this difference: