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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 17-19 of the Spring 2024 offering
of DSC 10.

Suppose that the trees on UCSD’s campus have a mean height of 100
feet and a **variance** of 36 feet. If the height of a
specific tree is 124 feet, what would its height be in standard units
for this distribution? Simplify your answer.

**Answer**: 4

The average score on this problem was 73%.

Let A be the answer to the previous question. Choose the best interpretation of A.

A randomly selected tree on UCSD’s campus has an A percent probability of being at least 124 feet tall.

A 124 foot tree is A times taller than the average tree on UCSD’s campus.

A 124 foot tree is A standard deviations taller than the average tree on UCSD’s campus.

At least 95% of trees on UCSD’s campus have a height within A standard deviations of the mean height.

**Answer**: A 124 foot tree is A standard deviations taller than the average
tree on UCSD’s campus.

The average score on this problem was 84%.

You are told that `scipy.stats.norm.cdf(-1.4)`

evaluates
to `0.08075665923377107`

. Suppose you have a standard normal
curve with mean at x=0 and standard
deviation 1. What is the area under the curve from x=0 to x=1.4? Give your answer as a number rounded
to 2 decimal places.

**Answer**: 0.42

The average score on this problem was 57%.

Suppose we measure the height in feet of a sample of trees on UCSD’s campus and use this sample to generate a 95% CLT-based confidence interval for the mean height of trees on campus. Let W be the width of this confidence interval.

If we instead were to measure the height of the same sample in inches, and again generate a 95% CLT-based confidence interval for the mean, what would be the width of this confidence interval in terms of W? There are 12 inches in 1 foot.

\dfrac{W}{12}

\dfrac{W}{\sqrt{12}}

W

12W

144W

**Answer**: 12W

The average score on this problem was 63%.

Which of the following quantities must be known in order to construct a CLT-based confidence interval for the population mean? Select all that apply.

Shape of the population (normal or not)

Shape of the sample (normal or not)

Mean of the population

Mean of the sample

Standard deviation of the population

Standard deviation of the sample

Size of the population

Size of the sample

**Answer**: Mean of the sample, Standard deviation of
the sample, Size of the sample

The average score on this problem was 73%.

We want to collect a sample of trees and use this sample to determine the proportion of all trees that are oak trees (a population parameter). We want to create a 95% confidence interval that is at most 0.04 wide. Which of the following inequalities should we use to find the smallest viable sample size we could collect?

\text{sample size} \geq (4 * \frac{0.5}{0.04})^2

\text{sample size} \geq (2 * \frac{0.5}{0.04})^2

\text{sample size} \geq (4 * \frac{1}{0.04})^2

\text{sample size} \geq (2 * \frac{1}{0.04})

**Answer**: \text{sample size}
\geq (4 * \frac{0.5}{0.04})^2

The average score on this problem was 52%.

Suppose that the trees on UCSD’s campus are 35% eucalyptus, 25% pine,
and the remaining 40% some other variety. Write **one line of
code** to simulate the act of randomly sampling 40 trees from
this distribution, with replacement. Your code should output an array of
length 3 where the elements represent the number of eucalyptus, pine,
and other trees, respectively.

**Answer**:
`np.random.multinomial(40, [0.35, 0.25, 0.40])`

The average score on this problem was 85%.