Question

please answer all three questions.

The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $16. Find the probability that a randomly selected utility bill is (a) less than $66, (b) between $81 and $90, and (c) more than $100. (a) The probability that a randomly selected utility bill is less than $66 is (Round to four decimal places as needed.)

Answer 1

16 Mean utility of city - $100- Standard deviation of utility 16.4 X Cost of utility bill. a) Req prob: P(x266) => pl X-100 < 66-100) 16 16 : C) Plz <-2-1.25.) where Z = X-10° UN COS 1.) -) 1-2:125) I Þ(x)+ Pl_n3=1]. 11- P12.125) 12.13) from normal table 1 (2.125) PIX<66): 1-0.9334) S = 0.01659 0.0166 by P( 81 < x < 90) => PC 81-100 < x - 100 290-100) P-1.18h 24-0.625). Z X -100 u N(o, a). Plz - 0.625)- Pla<-1.1875) -0-99341 16

- 1- P1220 626)-11 - Plze 1.18) - P(ZC11376) - P(220.625.) :) PL 2<119) - P(21063 7.B0:14) - $10-63.) from normal table (119)= 0.3 T D1063)-0-7333 Req probt 0.8930-07365 01.4 65. c) Req prob- P(X>100) - P(x - 1) 2. 91- P(X1100 laten Get :) | P/ 24o.) the 2=x-100 un(0, 1) 1-$10.) From normal table &co=0.5 - Дед рузь Reg Prob: 1-0.5000 -0.5000

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