### What is the probability of a normal random variable

Assignment Help Basic Statistics
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1. Professor Smith's statistics midterm had a mean of 85 and a standard deviation of 8. If a student got a score of 73, what was the student's standardized (z) score?

2. What is the probability of a normal random variable taking a value more than 1.6 standard deviations above its mean?

3. What is the probability that a normal random variable will take a value between 2 standard deviations below its mean and 1 standard deviation above its mean? [In other words, between Z = -2 and Z = 1]

4. The probability is .5 that a standardized normal variable takes a value below what particular value of Z?

5. The probability is .1515 that a standardized normal variable takes a value above what particular value of Z?

6. What two Z values, symmetric around the mean, will contain 75.4% of all Z values?

7. X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. What is the probability that X is less than 45?

8. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is a normal distribution with a mean of 70 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?

9. The owner of a fish market learns that the mean weight for salmon is 12.3 pounds, with a standard deviation of 3 pounds. Assuming that the weights of salmon are normally distributed, what is the probability that a randomly selected salmon will weigh less than 10 pounds?

10. (Use the salmon information from previous problem.) The middle 95% of salmon will weigh between ____ pounds and ____ pounds.

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