Chapter 6: Q 16 (page 385)
Suppose X ~ N(8, 1). What value of x has a z-score of –2.25?
Short Answer
The value of is
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Chapter 6: Q 16 (page 385)
Suppose X ~ N(8, 1). What value of x has a z-score of –2.25?
The value of is
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Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.
a. In words, define the random variable X.
b. X ~ _____(_____,_____)
c. If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. Sketch the graph and write the probability statement.
d. Sixty percent of all trials of this type are completed within how many days?
IQ is normally distributed with a mean of and a standard deviation of . Suppose one individual is randomly chosen. Let of an individual.
a.
b. Find the probability that the person has an IQ greater than . Include a sketch of the graph, and write a probability statement
c. MENSA is an organization whose members have the top of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement.
d. The middle of IQs fall between what two values? Sketch the graph and write the probability statement.
A NUMMI assembly line, which has been operating since , has built an average of cars and trucks a week. Generally, of the cars were defective coming off the assembly line. Suppose we draw a random sample of cars. Let represent the number of defective cars in the sample. What can we say about in regard to the empirical rule (one standard deviation, two standard deviations and three standard deviations from the mean are being referred to)? Assume a normal distribution for the defective cars in the sample.
Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?
Use the following information to answer the next four exercises:
Find the probability that
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