Making handcrafted pottery usually takes two major steps:wheel throwing and firing. The time of wheel throwing and thetime of firing are normally distributed random variables with meansof 40 min and 60 min and standard deviations of 2 min. and 3 min, respectively.

(a) What is the probability that a piece of pottery will befinished within 95 minutes?

(b) What is the probability that it will take longer than 110minutes?

Given Information:  

Mean = μ = 40 + 60 = 100 minutes  

Standard deviation = σ = 2² + 3² = 13 minutes  

Required Information:  

a. P(X < 95) = ?

b. P(X > 110) = ?

a. P(X < 95) = 0.0823

b. P(X > 110) = 0 .0028

Explanation:  

a)

Let random variable X represents the time in minutes of wheel throwing and firing.

The probability that a piece of pottery will be finished within 95 minutes means,

P(X < 95) = P(Z < (x - μ)/√σ)  

P(X < 95) = P(Z < (95 - 100)/√13)  

P(X < 95) = P(Z < -1.39)  

The z-score corresponding to -1.39 is 0.0823

P(X < 95) = 0.0823

Therefore, there is 8.23%  probability that a piece of pottery will be finished within 95 minutes.

b)

P(X > 110) = 1 - P(X < 110)  

P(X > 110) = 1 - P(X < (x - μ)/√σ)

P(X > 110) = 1 - P(X < (110 - 100)/√13)

P(X > 110) = 1 - P(X < 2.77)

The z-score corresponding to 2.77 is 0.9972

P(X > 110) = 1 - 0.9972

P(X > 110) = 0 .0028

Therefore, there is 0.28%  probability that a piece of pottery will take longer than 110 minutes.

answer: the correct answer is -32

step-by-step explanation: