Question

At a restaurant the time between two consecutive to-go orders is exponentially distributed with a rate of λ = 0.05/min.
Answer the following questions - round to 3 significant digits after decimal.

If a to-go order has just come, what is the probability that the next order will come in less than 17 minutes? 0.573 Computer's answer now shown above. You are correct. Previous Tries Your receipt no. is 158-3296 For quality control study, a random sample of 47 to-go orders is taken. What is the expected value of the sample average time between two consecutive to-go orders? 20.000 Computer's answer now shown above. You are correct. Your receipt no. is 158-9138 Previous Tries For quality control study, a random sample of 47 to-go orders is taken. What is the standard deviation of the sample average time between two consecutive to-go orders? 2.917 Computer's answer now shown above. You are correct. Previous Tries Your receipt no. is 158-8465 For quality control study, a random sample of 47 to-go orders is taken. What is the probability that the sample average time between two consecutive to-go orders, will be within 1 minute of the mean time? Submit Answer Tries 0/5

Answer 1

Lot x denate the time between two congecutive to go asders, nese, X follows exponential distbertion ceerth rate d= 0.05 pes mincele. then i 70 E(X) = * -dos a 20 vest se (0.0512 hore, na 47 which is large, lasge, Hence by Contral limit theorem. X • N( 90 tºo). fx(x) = sex = 400

NOW P [Sample aresage time between teo Conseatine too qo aldest i will be within a minute of the mean time P[20-1<20+1] =P[alg<x< 210 9 20 az 21-20 - Toe ८ 'Z 2 Joeln 14.00 1409 eP 1-0-34 0:342783 a 220.3427837 = P(Z <0.342783] - P(Z <-0-342 783] = 0.634119-6.365881 = 0.268238 ~ 0.268