Question

Let us assume that the variable Total_Rooms follows the normal distribution with mean 87 and standard deviation 95.1. Then: 4.1 Compute the probability that a randomly selected hotel has more than 100 rooms. 4.2 Compute the probability that a randomly selected hotel has between 60 and 80 rooms. 4.3 Find what is the minimum number of rooms a hotel should have in order to be considered in the 20% of the largest in size?

Answer 1

Solution Given tho1 87 6 = 95.1 4.1 PCXO0 - Cx100) 1-P oo 7 6 95-1 3 1-P 95. -P(NZ014 o.5557 1- O.444 3 o. 4443 Probobisity 4.2) PC6 00 80 ) P60-27 0-87 9 5.1 951 - 7 = P - 27 95.1 95.1 P (-0.282< -0.07) - PCz<-0.07)- P(z<-0.28 o.4721 .389 7 O. og 24 o. a224 Poobobisity

4.3 Using stoodosd normal +ab1e 20/ 1- P(2<z) PC2<z) PCZLO.842 G. 0.2 O.8 = 1O.2 = 0.84 2 Z Using -scoae formulo 0.842 x 95.1 +8 7 167.6 7 a hotei s hould Do of roomS inimum Cansidered 01dea in losgest size is 167.07 207