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