Question

1. determine whether the given value is from a discrete or continuous data set. the temperature of a cup of coffee is 67.3°f. a) discrete b) continuous 8) classify the histogram as skewed to the left, skewed to the right, or approximately symmetric. a) skewed to the left b) skewed to the right c) approximately symmetric 9) one hundred students are shown an eight - digit number on a piece of cardboard for three seconds and are asked to then recite the number from memory. the process is repeated until the student accurately recites the entire number from memory. the following histogram presents the number of trials it took each student to memorize the number. how many students memorized the number in three trials or less? a) 3 b) 17 c) 13 d) 87

Explanation:

Question 7

Step1: Recall data types

Discrete data: distinct, countable values. Continuous data: measurable, infinite values (e.g., temperature, height).

Step2: Analyze temperature

Temperature of coffee (67.3°F) is a measurable quantity with infinite possible values (can have decimals). So it's continuous.

Step1: Recall skewness

Left-skewed: tail on left (low values). Right-skewed: tail on right (high values). Symmetric: balanced.

Step2: Analyze histogram

The histogram has a tail on the left (shorter bars on left, taller on right). So it's skewed to the left? Wait, no—wait, the bars increase towards the right? Wait, no, the graph (as described: bars start short, get taller, then maybe? Wait, the standard: if the tail is on the left (low end), it's left-skewed (mean < median). Wait, the histogram shown: the bars are shorter on the left (low x-values) and taller on the right? No, wait, the user's diagram: "a histogram with bars increasing, then a tall bar, then...". Wait, no—wait, the options: A) left-skewed, B) right-skewed, C) symmetric. Wait, if the tail is on the left (the left side has shorter bars, so the tail is left), so it's skewed to the left? Wait, no—wait, skewness: the direction of the tail. So if the tail is on the left (low values), it's left-skewed (negative skewness). So the histogram here has a tail on the left (shorter bars on left), so skewed to the left? Wait, no, maybe I got it reversed. Wait, right-skewed: tail on right (high values), left-skewed: tail on left (low values). So if the bars are taller on the right and shorter on the left, the tail is on the left, so left-skewed? Wait, no—wait, let's think again. For example, a left-skewed distribution has the majority of data on the right, tail on left. So the histogram here: the bars start short (left) and get taller (right), so the tail is on the left. So it's skewed to the left? Wait, but the options: A) skewed to the left, B) right, C) symmetric. Wait, maybe the diagram is different. Wait, the user's diagram: "a histogram with bars increasing, then a tall bar, then...". Wait, maybe I made a mistake. Wait, no—wait, the correct approach: if the tail is on the left (the left side has the longer tail), then it's left-skewed. So the answer is A) skewed to the left? Wait, no, maybe the histogram is skewed to the left? Wait, no, let's check again. Wait, the standard: left-skewed (negative skew) has tail on left, right-skewed (positive skew) tail on right. So if the bars are shorter on the left (tail on left), then left-skewed. So the answer is A) skewed to the left? Wait, but maybe the diagram is different. Wait, the user's diagram: "a histogram with bars starting short, then increasing, then a tall bar, then...". Wait, maybe I misread. Wait, the correct answer: if the tail is on the left, it's left-skewed. So the answer is A) skewed to the left? Wait, no, maybe the histogram is skewed to the left. So I'll go with A.

Step1: Identify trials ≤3

We need students with trials =1, 2, 3.

Step2: Sum frequencies

From the histogram:

• Trials=1: 1 student (bar height 1)
• Trials=2: 2 students (bar height 2)
• Trials=3: 10 students (bar height 10)

Wait, no—wait, the x-axis: Number of Trials (1,2,3,4,...). The y-axis: Frequency.
Looking at the histogram:

• Trials=1: frequency 1 (bar at x=1, y=1)
• Trials=2: frequency 2 (bar at x=2, y=2)
• Trials=3: frequency 10? Wait, no, the user's histogram: "1, 2, 10, 26, 32, 15, 12, 3" for trials 1-8? Wait, the labels: x=1: 1, x=2: 2, x=3: 10, x=4:26, etc. Wait, the question: "three trials or less" means trials=1, 2, 3.

So sum: 1 (trial 1) + 2 (trial 2) + 10 (trial 3)? Wait, no, the options are A)3, B)17, C)13, D)87. Wait, maybe I misread the histogram. Let's re-express:

From the histogram:

• Trials=1: frequency 1
• Trials=2: frequency 2
• Trials=3: frequency 10? No, wait the options: A)3, B)17, C)13, D)87. Wait, maybe the frequencies are:

Trials=1: 1, Trials=2: 2, Trials=3: 10? No, 1+2+10=13, but option C is 13? Wait, no, the options: A)3, B)17, C)13, D)87. Wait, maybe I made a mistake. Wait, the x-axis: "Number of Trials" with labels 1,2,3,4,5,6,7,8,9. The y-axis: Frequency. The bars:

• At trial 1: frequency 1 (bar height 1)
• At trial 2: frequency 2 (bar height 2)
• At trial 3: frequency 10 (bar height 10)? No, 1+2+10=13, which is option C? Wait, no, option C is 13. Wait, but let's check again. Wait, maybe the frequencies are:

Trial 1: 1, Trial 2: 2, Trial 3: 10. Sum: 1+2+10=13. So answer C)13.

Answer:

B. Continuous

Question 8