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This quiz was administered in-person. It was closed-book and closed-note; students were not allowed to use the DSC 10 Reference Sheet. Students had 20 minutes to work on the quiz.

This quiz covered Lectures 13-18 of the Spring 2026 offering of DSC 10.

Regal jumping spiders (Phidippus regius) are gaining popularity as pets, and are known for their ability to jump many times more than their body length. Sofia’s sister has a pet jumping spider named Elise, whose jumps we will study in this quiz.

The elise DataFrame contains 400 rows (i.e. recorded jumps) and has the following columns:

• "distance" (int): the horizontal distance, in millimeters, of Elise’s jump
• "time" (str): the time of day during which the jump occurred—either "morning", "afternoon", or "night"
• "humidity" (int): the percent humidity of Elise’s enclosure, at the time of the jump

Problem 1

Jumping spiders prefer humidity to be between 50 and 70 percent. Suppose the "humidity" column has mean 60, and the range [48, 72] is the smallest range guaranteed to contain at least 75\% of the values in "humidity". What is the standard deviation of "humidity"?

Problem 2

Problem 2.1

Elise tends to be most active during the afternoon. Fill in the blanks below to produce 10,000 bootstrapped estimates of Elise’s mean jumping distance during the afternoon. Store these estimates in the array aft_means.

aft = elise[__(a)__]
aft_means = np.array([])

for i in np.arange(10000):
    resample = __(b)__
    estimate = resample.get("distance").mean()
    aft_means = __(c)__

Problem 2.2

Write code to compute the endpoints of a 70\% bootstrapped confidence interval for Elise’s mean afternoon jumping distance, using the values in aft_means.

left = __(d)__
right = __(e)__

Problem 3

A jump is considered a long jump if it is at least 100 millimeters in length. Sofia creates a new DataFrame called long, containing only the rows in elise that correspond to long jumps. Suppose the distribution of the "distance" column in long is approximately normal, with mean 144 and variance 36.

Problem 3.1

Fill in the blank to add a new column to long called "distance_su", containing the same information as the "distance" column but converted to standard units.

standard_units = __(a)__
long = long.assign(distance_su = standard_units)

Problem 3.2

Is "distance_su" approximately normally distributed?

• Yes

• No

Problem 3.3

Assume we have run from scipy import stats. Using stats.norm.cdf, write a Python expression that evaluates to the approximate proportion of distances in long that are at least 140 millimeters.

Problem 3.4

The data in long can be thought of a sample from the population of all long jumps that Elise takes. Suppose we use the data in long to create a 95% CLT-based confidence interval for the mean distance of all long jumps by Elise (a population parameter). The resulting interval is wider than we’d like, so we decide to collect a new sample that is just large enough to guarantee that the width of the resulting 95% confidence interval is no more than \frac32, assuming the new sample has the same standard deviation as the original. How large of a sample should we take? Give your answer as an integer.

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