Question

Q3. A customer spending waiting time at Alahwal_Jeddah check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. Suppose that a random sample of n = 49 customers is observed. Find the probability that the average time waiting in line for these customers is: (a) Less than 9.3 minutes (b) Between 5 and 10 minutes (c) Less than 7.5 minutes

Answer 1

- X, X, ... Xo N N tu, 62). Lindi Elxl. E lá Exi]; } 2£(xi) all Var (x) = var (+ 2 x 2 = 1 . no2 82 Here. n = 49 u = 8.2, 6= 1.5. Heme. X = Arexye of Sample - im Normal (4= 8.2, o=15 x - 8.2 V49 = 0.2143 q= 0.2143 N N (0, 1). $(x) = P 426x); $(-) 1-$(6) since n is large, we can assume nonnality P ( < 9.3) E p (z . 9. 38.2 0. 2143 = § (5.133) p sex < 10) PT 5-8.2 ezer - 0.2143_ $ 1813994) - $ 714.9323) 10 f. 2 1 0214

Ф (е. 94ч) - 1 + + ( ч. 923). - 1 - 1 + 1 - г ( x < эх) 1 2 - 1 ) o 21м / P ( 2 – 3. 266) Ф – 3. 2669) - 1 - Ф ( 3. 26)- 1 - о. 999 - = [О. оо].