Math 54 Section 7.1 and 7.2
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Math 54
Section 7.1 and 7.2
1. High temperatures in a certain city for the month of August follow a uniform distribution over the interval 63°F to 90°F. What is the probability that a randomly selected August day has a high temperature that exceeded 68°F?
2. Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 30 to 80. What is the probability that this experiment results in an outcome less than 40?
3. Find the area under the standard normal curve to the left of z = 1.25.
4. Find the area under the standard normal curve between z = 1 and z = 2.
5. Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation σ =
12. Compute the probability P(37 < X < 85).
6. Assume that the random variable X is normally distributed, with mean μ = 100 and standard deviation σ =
20. Compute the probability P(X > 116).
7. A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 50 seconds. Find the probability that a
randomly selected boy in secondary school will take longer than 325 seconds to run the mile.
8. Find the z-score for which the area under the standard normal curve to its left is 0.96
2022-05-21