6. The time it takes latex paint to dry is normally distributed. If the mean is

Question

6. The time it takes latex paint to dry is normally distributed. If the mean is 3.5 hours with a standard deviation of 45 minutes, find the probability that the drying time will be as follows: a) less than 2 hours 15 minutes

b) between 3 and 4 hours

Hint: convert to either hours or minutes first

7. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?

Please give me the answer with detailed explanation. I have no idea about this.

Explanation / Answer

6.a)For X=2.15, z=(X-mu)/sigma

=(2.15-3.5)/0.75, sigma=45/60=0.75 hours

=-1.8

P(<2.15)=P(z<-1.8)=0.0359

b)for X=3, z=(3-3.5)/0.75=-0.67

For X=5, z=(5-3.5)/0.75=2

Thus the required probability is P(3<X<5)

=P(X<5)-P(X<3)

=P(z<2)-P(z<-0.67)

=0.9772-0.2514

=0.7258

7.For X=3, z=(3-3.2)/0.8

=-0.25

For X=5, z=(5-3.2)/0.8

=2.25

P(3<X<5)

=P(X<5)-P(X<3)

=P(z<2.25)-P(Z<-0.25)

=0.9878-0.4013

=0.5865

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