# 1 the probability that a standard normal random

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Chapter 11 / Exercise 25
Applied Calculus
Berresford/Rockett
Expert Verified
1. The probability that a standard normal random variable, Z , falls between – 1.50 and 0.81 is 0.7242. 2. The probability that a standard normal random variable, Z , is below 1.96 is 0.4750. 3. The probability that a standard normal random variable, Z , falls between –2.00 and –0.44 is 0.6472. 4. A worker earns \$15 per hour at a plant and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is \$5 per hour, the average wage for the plant is \$7.50 per hour. 5. Any set of normally distributed data can be transformed to its standardized form. 6. The "middle spread," that is the middle 50% of the normal distribution, is equal to one standard deviation. 7. If a data batch is approximately normally distributed, its normal probability plot would be S-shaped.
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Chapter 11 / Exercise 25
Applied Calculus
Berresford/Rockett
Expert Verified
4 S ECTION III: F REE R ESPONSE P ROBLEMS 1. 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 approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. a. What proportion of the plan recipients would receive payments beyond age 75? b. Find the age at which payments have ceased for approximately 86% of the plan participants. 2. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces. 3. 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 less than 2.2 pounds is _______? 4. The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and σ = 25 grams. a. What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine? b. What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine? c. µ