Question

1.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P ( − b < z < b ) = 0.6724 , find 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 to b ? (given in the problem) What is the area under the normal curve that is NOT between − b and b ? (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 ? (Use symmetry of normal distribution.) Given that information, what calculator function can you use to find − b ? Now find b .

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

If P(z<e)=0.0141P(z<e)=0.0141, find e.

e= (Round to four decimal places.)

3.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.)

4.A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 188.7-cm and a standard deviation of 1.5-cm.

Find P₈₁, which is the length separating the shortest 81% rods from the longest 19%.
P₈₁ = -cm

Enter your answer as a number accurate to 1 decimal place.

5.The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 17 days. A distribution of values is normal with a mean of 264 and a standard deviation of 17.

What percentage of pregnancies last fewer than 220 days?
P(X < 220 days) =  %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

6.A distribution of values is normal with a mean of 219.4 and a standard deviation of 29.9.

Find P₉₉, which is the score separating the bottom 99% from the top 1%.
P₉₉ =

Enter your answer as a number accurate to 1 decimal place.

Answer 1