The time taken to prepare the envelopes to mail a weekly report to all executives in a company has a normal distribution, with a mean of 35 minutes and a standard deviation of 2 minutes. On 95% of occasions the mailing preparation takes less than a) 38.29 minutes b) 31.71 minutes c) 35.25 minutes d) 34.75 minutes

Mailing preparation takes 38.29 min max time to prepare the mails.

Step-by-step explanation:

Given:

Mean:35 min

standard deviation:2 min

and 95%  confidence interval.

To Find:

In normal distribution mailing preparation time  taken less than.

i.eP(t<x)=?

Solution:

Here t -time and x -required time

mean time 35 min

5 % will not have true mean value . with 95 % confidence.

Question is asked as ,preparation takes less than  time means what is max time that preparation will take to prepare mails.

No mail take more time than that time .

by Z-score or by confidence interval is

Z=(X-mean)/standard deviation.

Z=1.96 at  95 % confidence interval.

1.96=(X-35)/2

3.92=(x-35)

X=38.29 min

or

Confidence interval =35±Z*standard deviation

=35±1.96*2

=35±3.92

=38.29 or 31.71 min

But we require the max time i.e 38.29 min

And by observation we can also conclude the max time from options as 38.29 min.