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Mail order a mail order company has a 10% success rate. If it mails advertisements to 602 people, find the probability of getting less than 57 sales. Round z value calculations to 2 decimal places and final answer to at least 4 decimal points

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Answer:

0.30854

Step-by-step explanation:

Given :

Sample size, n = 602

p = 10% = 0.1

q = 1 - p = 1 - 0.1 = 0.9

Using binomial approximation :

Mean, m = n * p = 602 * 0.1 = 60.2

Standard deviation, s = sqrt(npq) = sqrt(602*0.1*0.9) = 7.36

P(x < x - 0.5) = (x - m) / s

x = 57

P(x < 56.5) = (56.5 - 60.2) / 7.36

Z = - 3.7 / 7.36

Z = - 0.5027 = - 0.50

P(Z < - 0.50) = 0.30854 (Z probability calculator)

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