Question

2.

If P(A) = 0.4 and P(B) = 0.6, which of the following must be TRUE?

Select one:

A. Events A and B are collectively exhaustive.

B. None of the other three choices must be true.

C. Events A and B are mutually exclusive.

D. Events A and B are statistically independent.

3.A researcher reported that the 95% confidence interval for the mean ranged from 460 to 540. He knew that the population is normally distributed. He was sure that the mean of the sample was 500, the standard deviation of the sample was 160, but he could not remember the exact sample size. Can we help him out finding the sample size?

Answer 1

2. Given that, P(A)=0.4 and P(B)=0.6 from this information, correct/ true sentence is option B (None of the other three choices must be true), Because to check whether events are exhaustive or mutually exclusive or independent, we must know either or or .

3. In this problem, population is normally distributed.

here we know confidence interval =(460,540), mean = = 500 and

sample standard deviation = = 160. We have to calculate sample size i.e, n.

Formula of CI for mean is

We have CI= Upper limit=540 and Lower limit= 460, the z score for 95% confidence interval =1.96

So, the above formula become:

will calculate for lower limit:

So, n=(7.84)^2

Hence n=62.

So, Sample size is 62.

We can cross verify this sample size to calculate upper limit: