Q9. The histogram above shows the number of minutes needed by 45 students to finish playing a short game. Which of the following statements is correct?

Background

Topic: Describing Distributions

This question tests your ability to interpret the shape of a distribution from a histogram. You need to identify whether the distribution is skewed, bell-shaped, or uniform.

Key Terms:

• Skewed Right: The tail on the right side (higher values) is longer.

• Skewed Left: The tail on the left side (lower values) is longer.

• Bell-Shaped: The distribution is symmetric and resembles a normal curve.

• Uniform: All bars are approximately the same height.

Step-by-Step Guidance

1. Examine the histogram and note the frequencies for each time interval.

2. Identify where the majority of the data is concentrated (which intervals have the highest frequencies).

3. Observe the tails of the distribution: Is there a longer tail on the left or right?

4. Compare the heights of the bars to determine if the distribution is symmetric, skewed, or uniform.

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Q10. The histogram below displays the frequencies of waiting times, in minutes, for 175 patients in a dentist's office. Which of the following could be the median of the waiting time, in minutes?

Background

Topic: Measures of Center (Median)

This question tests your ability to estimate the median from a histogram. The median is the value that divides the data into two equal halves.

Key Terms:

• Median: The middle value when data is ordered.

• Histogram: A graphical representation of data distribution.

Step-by-Step Guidance

1. Calculate the total number of patients (175).

2. Find the position of the median: th patient.

3. Use the histogram to determine which interval contains the 88th patient by adding frequencies from left to right.

4. Estimate the median based on the interval where the cumulative frequency reaches or exceeds 88.

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Q28. Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?

Background

Topic: Probability of Independent Events

This question tests your understanding of how to calculate the probability of two independent events both occurring.

Key Terms and Formulas:

• Independent Events: Events where the outcome of one does not affect the other.

• Probability of both events:

Step-by-Step Guidance

1. Identify the probability that Joe buys no books: .

2. Identify the probability that Matthew buys no books: .

3. Since the events are independent, multiply the probabilities: .

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