Question

on a recent quiz, the class mean was 77 with a standard deviation of 3.9. calculate the z-score (rounded to 2 decimal places) for a person who received score of 90.
z-score:
is this unusual?
not unusual
unusual
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question 11
question statement
match each percentile with its corresponding term from the five-number summary.
input your response:
0th percentile a. minimum value
25th percentile b. ( q_1 )
50th percentile c. ( q_3 )
75th percentile d. median
100th percentile e. maximum value

Explanation:

Part 1: Calculate the z - score

Step 1: Recall the z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step 2: Identify the values

We are given that $x = 90$, $\mu=77$, and $\sigma = 3.9$.

Step 3: Substitute the values into the formula

Substitute $x = 90$, $\mu = 77$, and $\sigma=3.9$ into the formula: $z=\frac{90 - 77}{3.9}=\frac{13}{3.9}\approx3.33$ (rounded to 2 decimal places).

Step 4: Determine if the z - score is unusual

A z - score is generally considered unusual if its absolute value is greater than 2 or 3 (different conventions, but a z - score of 3.33 is greater than 3 in many cases). So, a z - score of 3.33 is unusual.

• The 0th percentile represents the smallest value in the data set, which is the minimum value.
• The 25th percentile is also known as the first quartile ($Q_1$).
• The 50th percentile is the median of the data set (it divides the data into two equal halves).
• The 75th percentile is also known as the third quartile ($Q_3$).
• The 100th percentile represents the largest value in the data set, which is the maximum value.

Answer:

z - score: $3.33$
Is this unusual? Unusual

Part 2: Match the percentiles with the five - number summary terms