1. Under specific conditions, the drying time of a certain type of paint is norm

Question

1. Under specific conditions, the drying time of a certain type of paint is normally distributed with a mean value of 55 minutes, and a standard deviation of 7 minutes. Use only the values given to you to solve this problem:

i (0.385) = 0.65, (0.428) = 0.67, (0.71) = 0.762, (1.43) = 0.924, (1.92) = 0.973.

ii 1 (0.972) = 1.917, 1 (0.740) = 0.643, 1 (0.95) = 1.645.

iii z0.0017 = 2.923, z0.016 = 2.14, z0.027 = 1.93.

(a) What is the probability that the paint will dry in 45 minutes or less?

(b) What is the probability that the paint will dry between 50 and 70 minutes?

(c) How many minutes represents the 35th percentile in paint drying?

Explanation / Answer

a) P(X<45)

Z =(X - 55)/7

z= (45-55)/7 = -1.42857143

hence

P(X<45) =(-1.43)

(1.43) = 0.924

hence (-1.43) =1- 0.924 = 0.076

b) P(50 <X< 70)

P(-0.71 <Z< 2.14) =

(2.14) - (-0.71) = (1 -0.016) -(1-0.762) = 0.746

c) X = 55 + z*7

P(Z< z) = 0.35

or P(Z < -z) = 0.65

as (0.385) = 0.65

-z = 0.385

z = -0.385

hence

55 -0.385 *7 = 52.305

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