Complete the below:
Part 1: Introduction to Normal Distribution and the Standard Normal Distribution
1. Use the Standard Normal Distribution table to find the indicated area under the standard normal curve.
a. Between z = 0 and z = 1.24
b. To the right of z = 1.09
c. Between z = -1.56 and z = -0.15
d. To the left of z = -1.93
Part 2: Normal Distributions: Find Probabilities
2. The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter less than 0.57?
3. The a loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 50. Find the probability that an applicant will have a rating less than 260.
Part 3: Normal Distributions: Finding Values
4. Answer the questions about the specified normal distribution.
a. The lifetime of ZZZ batteries are normally distributed with a mean of 280 hours and a standard deviation σ of 10 hours. Find the number of hours that represent the 25th percentile.
b. Scores on an English placement test are normally distributed with a mean of 50 and standard deviation σ of 2.5. Find the score that marks the top 10%.
Part 4:Sampling Distribution and the Central Limit Theorem
5. Find the probabilities.
a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 72 inches and a standard deviation σ of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be greater than 75 inches?
b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating less than 260?