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

Question

Mathematics

Mina Keith

26 August, 15:18

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

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Answers (1)

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Christine Medina · Answer 1

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
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.