Question

Stress at work: In a poll conducted by the General Social Survey, 78% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places. (a) Approximate the probability that 145 or fewer workers find their jobs stressful. (b) Approximate the probability that more than 159 workers find their jobs stressful. (c) Approximate the probability that the number of workers who find their jobs stressful is between 144 and 164 inclusive.

Answer 1

In a poll conducted by the general Social Surrey, 78% of respondent said that their Jobs were sometimes on always stressfull- So, if we take this as success, then owe success Pecobability is, po 78 = 0.78 We take a random samp m = 200 workers.. - We know, that, xe Number of seespondent- follows a Honormal distributions

As sample size is large we should use, approximation to Binomial. for this Ist we have to check if, sio and m(1-) >10. Now, here, 2007 0.78 = 158710 and n(1-P) 2 300(1-0-98), 44 y 10 So, we can use Normal appropimation, (a) Here we have to find the probability that - 145 on fewer workers find their job Stressfuli ie x < 145 on X 2 14505 By using continuity Hell Correction footon. des P ( x 2145.5) Now, since we approximate to Normal, theng mean Mz np z 200X0.78=156 and Standard deviation, 6e vnp (1-P) A n ti -1200X0.78*(1-0.38) - 25.86 so, PCX 21455) - Plytele z 1455.86152) 2 P(Z 2-1'79) -0.0367

(6) Here we have to find, P(x> 159) en PCX > 159.57 By using continuely Somouction factor PCX > 15915) -- P(x = 159-5) :21-P/XPRL153 -1- P(Z <0597) = 1-0.7224 - 0'2776 (C) Here we have to find the probability that, x is between 144 and 164 les P (144 Į Xe 164) on PC 143.5 4 X5 164.5) cometion-factón. 2 PCX5164.5) - P(x = 143.5) Platteg 16405-152 )- p/XH 1935152) a Plzs 1'45) - P(*s-2-13) = 0°9265 -0.0166 = 0.9099 5 using continuity