Final assignment | Algebra homework help

Question 1 (3 points)Algebra

Which of the following is the operation called standardizing?

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Question 2 (3 points)

Given that Z is a standard normal variable, the value z for which P(Z  z) = 0.2580 is

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Question 3 (3 points)

 is the:

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Question 4 (3 points)

Which of the following statements are true?

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Question 5 (3 points)

If two events are collectively exhaustive, what is the probability that one or the other occurs?

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Question 6 (3 points)

 The joint probabilities shown in a table with two rows, A₁and A₂ and two columns, B₁ and B₂, are as follows: P(A₁ and B₁) = .10, P(A₁ and B₂) = .30, P(A₂ and B₁) = .05, and P(A₂ and B₂) = .55. Then P(A₁|B₁), calculated up to two decimals, is

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Question 7 (3 points)

There are two types of random variables, they are

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Question 8 (3 points)

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:

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Question 9 (3 points)

If two events are independent, what is the probability that they both occur?

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Question 10 (3 points)

We assume that the outcomes of successive trials in a binomial experiment are:

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Question 11 (3 points)

The mean of a binomial distribution with parameters n and p is given by:

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Question 12 (3 points)

The mean  of a probability distribution is a:

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Question 13 (3 points)

One reason for standardizing random variables is to measure variables with:

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Question 14 (3 points)

In a continuous probability distribution, the total probability is spread over a continuum. What is the value of the total probability?

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Question 15 (5 points)

Consider a random variable X with the following probability distribution:

P(X=0) = 0.25, P(X=1) = 0.35, P(X=2) = 0.15, P(X=3) = 0.10, and P(X=4) = 0.15.

Find the mean and standard deviation of X.

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Question 16 (3 points)

Consider a random variable X with the following probability distribution:

P(X=0) = 0.08, P(X=1) = 0.22, P(X=2) = 0.25, P(X=3) = 0.25, P(X=4) = 0.15, P(X=5) = 0.05

Find P(X<2)

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Question 17 (3 points)

Suppose that 20% of the students of Big Rapids High School play sports. Moreover, assume that 55% of all students are female, and 15% of all female students play sports.

If we choose a student at random from this school, what is the probability that this student is a male who does not play sports?

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Question 18 (4 points)

The grades on the final examination given in a large organic chemistry class are normally distributed with a mean of 72 and a standard deviation of 8. The instructor of this class wants to assign an “A” grade to the top 10% of the scores, a “B” grade to the next 10% of the scores, a “C” grade to the next 10% of the scores, a “D” grade to the next 10% of the scores, and an “F” grade to all scores below the 60^th percentile of this distribution. For a letter grade of C, find the lowest acceptable score within the established range. Provide your answer in the format XX.X, for example 83.4.

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Question 19 (4 points)

The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.

What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

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Question 20 (3 points)

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. 

What is the probability that a randomly selected customer will spend exactly $28 at this store?

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Question 21 (3 points)

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. 

What is the probability that a randomly selected customer will spend less than $15 at this store?

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Question 22 (3 points)

If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to

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Question 23 (2 points)

Given that events A and B are independent and that P(A) = 0.8 and P(B/A) = 0.4, then P(A and B) = 0.32.

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Question 24 (2 points)

If A and B are independent events with P(A) = 0.40 and P(B) = 0.50, then P(A|B) is 0.50.

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Question 25 (2 points)

The number of television sets sold on a given day is a continuous random variable.

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Question 26 (2 points)

If P(A and B) = 0, then A and B must be collectively exhaustive.

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Question 27 (2 points)

Two or more events are said to be exhaustive if one of them must occur.

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Question 28 (2 points)

Two or more events are said to be mutually exclusive if at most one of them can occur.

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Question 29 (2 points)

The left half under the normal curve is slightly smaller than the right half.

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Question 30 (2 points)

The binomial distribution is a discrete distribution that deals with a sequence of identical trials, each of which has only two possible outcomes.

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Question 31 (2 points)

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

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Question 32 (2 points)

A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

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Question 33 (2 points)

Using the standard normal curve, the Z– score representing the 10th percentile is 1.28.

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Question 34 (2 points)

A random variable X is normally distributed with a mean of 100 and a variance of 25. Given that X = 110, its corresponding Z– score is 0.40.

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Question 35 (3 points)

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. If the meeting will be held only if every vice president can attend, what is the probability that the meeting will take place?

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Question 36 (3 points)

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 9 pounds and a standard deviation of 3 pounds.

If a dieter is selected at random, what is the probability that the dieter lost exactly 8 pounds?

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