A well-mixed cookie dough will produce cookies with a mean of 66 chocolate chips apiece. What is the probability of getting a cookie with at least 55 chips? Round your answer to four decimal places.

0.7262

Step-by-step explanation:

Let random variable = X

Probability of getting a cookie with at least 55 chips:

P(55≤ X ≤78), where X1 = 55 and X2 = 78

Let mean, U = 66 and  standard deviation, S.D. = 10

Let Z = X - U/S.D; Z1 = X1 - U/S.D and Z2 = X2 - U/S.D

Z1 = 55 - 66/10 = - 1.1

Z2 = 78 - 66/10 = 1.2

P(X1≤ X ≤ X2) = P(X1 -U/S.D ≤ X - U/S.D ≤ X2 - U/S.D)

P(Z1 ≤ Z ≤ Z2) = P(0 ≤ Z ≤ Z1) + P(0 ≤ Z ≤ Z2)

Hence, (55 ≤ X ≤ 78) = P( - 1.1 ≤ Z ≤ 1.2)

∴ P(-1.1 ≤ Z ≤ 1.2) = P(0 ≤ Z ≤ 1.1) + (0 ≤ Z ≤ 1.2)

=   0.3413 + 0.3849 = 0.7262

step-by-step explanation:

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