Arandom sample of size n1equals25, taken from a normal population with a standard deviation sigma1equals6, has a mean x overbar 1equals87. a second random sample of size n2equals33, taken from a different normal population with a standard deviation sigma2equals4, has a mean x overbar 2equals36. find a 96% confidence interval for mu1minusmu2.

The 96% confidence interval would be given by  

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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".  

represent the sample mean 1

represent the sample mean 2

n1=25 represent the sample 1 size  

n2=33 represent the sample 2 size  

sample standard deviation for sample 1

sample standard deviation for sample 2

parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:  

(1)  

The point of estimate for is just given by:

Since the Confidence is 0.96 or 96%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.02,0,1)".And we see that  

The standard error is given by the following formula:

And replacing we have:

Confidence interval

Now we have everything in order to replace into formula (1):  

So on this case the 96% confidence interval would be given by  

the correct answers i think are b. and d.

give me brainliest if it is correct!