Question

dont understand

0 A binomial experiment consists of 500 trials. The probability of success for each tills 0.5 What is the probability of obtaining 240-270 successes? Approximate the probability using a normal distribution (This binomial experiment easily passes the rule of thumb test for approximating a binomial distribution using a normal distribution, as you can check When computing the probability, adjust the given interval by extending the range by 05 on each side) Click the icon to view the area under the standard normal curve table The probability of obtaining 240-270 success is approximately (Round to two decimal places as needed) e FE $ 4 a & 7 % 5 6 8 3 E R. T Tab Q J K L G H A S DF Caps Lock

Answer 1

Solution:

We are given

n = 500

p = 0.5

q = 1 - p = 1 - 0.5 = 0.5

µ = Mean = np = 500*0.5 = 250

σ = SD = Sqrt(npq) = sqrt(500*0.5*0.5) = 11.18034

We have to find P(240≤X≤270) ≈ P(239.5 < X < 270.5)

P(239.5 < X < 270.5) = P(X<270.5) - P(X<239.5)

Z = (X - µ)/σ

Z = (270.5 - 250)/ 11.18034

Z = 1.833576

P(Z<1.833576) = P(X<270.5) = 0.966642

(You can find this probability by using z-table/Ti-84/83 calculator/excel/software/etc.)

Now find P(X<239.5)

Z = (239.5 - 250)/ 11.18034

Z = -0.93915

P(Z<-0.93915) = P(X<239.5) = 0.173827

(by using z-table)

P(239.5 < X < 270.5) = P(X<270.5) - P(X<239.5)

P(239.5 < X < 270.5) = 0.966642 - 0.173827

P(239.5 < X < 270.5) = 0.792815

The probability of obtaining 240-270 successes is approximately 0.79.