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2 answers:
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Answer:
And using the normal standard table or excel we find the probability:
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 avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then, the distribution for the sample mean is given by:
We select a sample of n =50 people. And we want to find the following probability
And using the normal standard table or excel we find the probability:
Answer:
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Step-by-step explanation:
Consider the provided information.
Machine A can fill an order of widgets in a hours. Machine B can fill the same order of widgets in b hours.
Thus, in 1 hr machine A's work is 1/a and machine B's work is 1/b.
We need to find whether the Machine A's rate the same as that of Machine B?
Statement 1: Machines A and B finish the order at exactly 4:48 p.m.
Total time, A and B worked = 4:48 = 4+ hrs = 4+
hrs=
hours
Thus,
Let say Machine A's rate the same as that of Machine B
It is given that a and b are even integers, but is not an even integer.
Hence, Machine A's rate is not same as that of Machine B.
Therefore, statement (1) ALONE is sufficient.
Statement 2:
There are many possible case in which a and b are even integer and there sum is 20.
If a = b = 10 (both even), then Machine A's rate is same as that of Machine B.
if a = 6 and b = 14 (both even), then Machine A's rate is not same as that of Machine B.
Therefore, No unique answer with statement 2.
Hence, statement 2 alone is not sufficient.