one university, the mean distance commited to campus by stubenits is 19.0 milles, with a standand deviation of 5.1 miles. Suppose that the cummute
ances are nomally distributed. Complete the following statements.
(a) Approximately of the studenits have commute distances between
and miles.
(b) Approximates
miles and 34.3 miles.

Question

one university, the mean distance commited to campus by stubenits is 19.0 milles, with a standand deviation of 5.1 miles. Suppose that the cummute
ances are nomally distributed. Complete the following statements.
(a) Approximately

of the studenits have commute distances between
and

miles.
(b) Approximates
miles and 34.3 miles.

UpStudy AI · Accepted Answer

(a) Using the empirical rule, approximately 95% of the students’ commute distances lie within 2 standard deviations of the mean. That is, between
$$
19 - 2(5.1) \quad \text{and} \quad 19 + 2(5.1).
$$
Calculating these limits:
$$
19 - 2(5.1) = 19 - 10.2 = 8.8 \quad \text{miles},
$$
$$
19 + 2(5.1) = 19 + 10.2 = 29.2 \quad \text{miles}.
$$
So, approximately 95% of the students have commute distances between $$8.8$$ miles and $$29.2$$ miles.

(b) Similarly, approximately 99.7% of the students’ commute distances lie within 3 standard deviations of the mean. Since the upper limit is given as $$34.3$$ miles,
$$
19 + 3(5.1) = 34.3 \quad \text{miles}.
$$
We find the lower limit by calculating:
$$
19 - 3(5.1) = 19 - 15.3 = 3.7 \quad \text{miles}.
$$
Thus, approximately 99.7% of the students have commute distances between $$3.7$$ miles and $$34.3$$ miles.
(a) Approximately 95% of the students have commute distances between 8.8 miles and 29.2 miles. (b) Approximately 99.7% of the students have commute distances between 3.7 miles and 34.3 miles.

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