Question

8.The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 5.6 liters. What is the probability that daily production is between 30.9 and 46.1 liters? (Round your answer to 4 decimal places.)

9.A particular fruit's weights are normally distributed, with a mean of 788 grams and a standard deviation of 36 grams. If you pick one fruit at random, what is the probability that it will weigh between 690 grams and 910 grams? (Round answer to four decimal places.)

10.A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 0.7 inches. If one item is chosen at random, what is the probability that it is less than 6.9 inches long? (Round to four decimal places.)

11.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(zc)=0.3131P(z>c)=0.3131 c= (Round to two decimal places.)

12.For a standard normal distribution, find:

P(z>c)=0.3131P(z>c)=0.3131

c=

(Round to two decimal places.)

13.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.6724P(-b<z<b)=0.6724, find b.

b=b=  (Round to two decimal places.)

Hint: Consider symmetry on this problem and draw a picture of the normal distribution to visualize this problem.

• What is the area under the normal curve from −b-b to bb? (given in the problem)
• What is the area under the normal curve that is NOT between −b-b and bb? (Complement of the answer to the first part of the hint)
• Given that information, what is the area under the normal curve from −∞-∞ to −b-b? (Use symmetry of normal distribution.)
• Given that information, what calculator function can you use to find −b-b?
• Now find b.

14.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(0<z<a)=0.4932P(0<z<a)=0.4932, find a.

a=

(Round to two decimal places.)

Answer 1