Review Test

Front

If four coins are tossed, which is NOT a possible value of the random variable for the number of heads?

Back

5

Answer explanation

In an experiment of tossing 4 coins, the possible outcomes for the number of heads are {0, 1, 2, 3, 4}. It is physically impossible to get 5 heads from only 4 coins.

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https://www.youtube.com/watch?v=wRSKNyUXw4c&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=1

Front

Which of the following is a continuous random variable? Number of students in a classroom , The weight of a bag of rice , Number of cars in a parking lot, Total pages in a textbook

Back

The weight of a bag of rice

Answer explanation

Weight is a continuous variable because it is measured and can take on any value within a range (e.g., 5.25 kg). Other options are discrete because they are counted in whole numbers.

See this video to master this topic:
https://www.youtube.com/watch?v=wRSKNyUXw4c&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=1

Front

Which formula gives the probability distribution shown by the following table?

Back

P(X) = X / 10

Answer explanation

By substituting the X values into the formula P(X) = x /10, we get the exact values in the table: 1/10, 2/10, 3/10, and 4/10. The sum of these probabilities is 10/10 = 1, which confirms it is a valid distribution.

See this video to master this topic:
https://www.youtube.com/watch?v=fH6TMTSpGMA&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=2

Front

How many ways can a sum of 4 come out when you roll two dice?

Back

3

Answer explanation

To get a sum of 4, the possible outcomes are (1,3), (2,2), and (3,1). There are exactly 3 ways this can happen.

See this video to master this topic:
https://www.youtube.com/watch?v=fH6TMTSpGMA&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=2

Front

This is a table or list of all possible values of a random variable together with their corresponding probabilities.

Back

Probability Distribution

Answer explanation

A Probability Distribution is specifically defined as the list or table that pairs every value of a random variable with its probability of occurring.

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https://www.youtube.com/watch?v=fH6TMTSpGMA&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=2

Front

What is TRUE regarding the total area under the standard normal curve?

Back

The total area is exactly 1.

Answer explanation

A fundamental property of any probability density function, including the standard normal curve, is that the total area under the curve is exactly 1.

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https://www.youtube.com/watch?v=uVcEj6_UJGo&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=8

Front

A random variable X has a mean of 50 and a standard deviation of 5. What is the corresponding z-score for x = 40?

Back

-2.0

Answer explanation

Using the formula $z = \frac{x - \mu}{\sigma}$, we calculate: $z = \frac{40 - 50}{5} = \frac{-10}{5} = -2.0$. The negative sign indicates the value is below the mean.

See this video to master this topic:
https://www.youtube.com/watch?v=3zKtkjt-oxQ&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=9

Front

What is the area under the normal curve if the z-score given is -1.25?

Back

0.1056

Answer explanation

Looking up z = -1.25 in a standard normal distribution table (left-tail area) provides the value 0.1056.

See this video to master this topic:
https://www.youtube.com/watch?v=GxcV2xNZNqM&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=11

Front

What is the z-value if the area to the left is 0.0250?

Back

-1.96

Answer explanation

When searching for the area 0.0250 in the body of a z-table, it corresponds to the row -1.9 and the column .06, resulting in z = -1.96.

See this video to master this topic:
https://www.youtube.com/watch?v=GxcV2xNZNqM&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=11

Front

Using the standard normal curve, what is the approximate area of P(-1.50 < Z < 1.50)?

Back

0.8664

Answer explanation

The area for z = 1.50 is 0.9332 and for z = -1.50 is 0.0668. To find the area between them: 0.9332 - 0.0668 = 0.8664.

See this video to master this topic:
https://www.youtube.com/watch?v=GxcV2xNZNqM&list=PLFG5lKeDCYPmV1IFZFpBG-oyVzo0Gnbom&index=11