Answer:
The probability that a piece of pottery will be finished within 95 minutes is 0.0823.
Step-by-step explanation:
We are given that the time of wheel throwing and the time of firing are normally distributed variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.
Let X = time of wheel throwing
So, X ~ Normal()
where, = mean time of wheel throwing
= standard deviation of wheel throwing
Similarly, let Y = time of firing
So, Y ~ Normal()
where, = mean time of firing
= standard deviation of firing
Now, let P = a random variable that involves both the steps of throwing and firing of wheel
SO, P = X + Y
Mean of P, E(P) = E(X) + E(Y)
= 40 + 60 = 100 minutes
Variance of P, V(P) = V(X + Y)
= V(X) + V(Y) - Cov(X,Y)
=
{Here Cov(X,Y) = 0 because the time of wheel throwing and time of firing are independent random variables}
SO, V(P) = 4 + 9 = 13
which means Standard deviation(P), =
Hence, P ~ Normal()
The z-score probability distribution of the normal distribution is given by;
Z = ~ N(0,1)
where, = mean time in making pottery = 100 minutes
= standard deviation =
minutes
Now, the probability that a piece of pottery will be finished within 95 minutes is given by = P(P 95 min)
P(P 95 min) = P(
) = P(Z
-1.39) = 1 - P(Z < 1.39)
= 1 - 0.9177 = <u>0.0823</u>
The above probability is calculated by looking at the value of x = 1.39 in the z table which has an area of 0.9177.