Find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as "minutes") in your results. The following data represent the duration (in minutes) of workout sessions completed by a group of individuals at a fitness center over a week:

$\text{30, 45, 60, 50, 40, 55, 70, 35, 65, 50, 42}$

What do the results tell us about the variation in workout durations?

Below are the battery life durations (in hours) for 25 different laptops.

| 2.1 | 2.3 | 2.5 | 2.7 | 3.0 |

| 3.2 | 3.4 | 3.6 | 3.8 | 4.0 |

| 4.2 | 4.5 | 4.7 | 4.9 | 5.1 |

| 5.3 | 5.5 | 5.7 | 5.9 | 6.2 |

| 6.4 | 6.6 | 6.8 | 7.0 | 7.5 |

Find the percentile corresponding to the 4.5 hours battery life.

Use the given list of the battery life durations (in hours) for 25 different laptops to find the value of the quartile indicated below.

| 2.1 | 2.3 | 2.5 | 2.7 | 3.0 |

| 3.2 | 3.4 | 3.6 | 3.8 | 4.0 |

| 4.2 | 4.5 | 4.7 | 4.9 | 5.1 |

| 5.3 | 5.5 | 5.7 | 5.9 | 6.2 |

| 6.4 | 6.6 | 6.8 | 7.0 | 7.5 |

Q3

The weights (in grams) of a sample of apples randomly sorted from a basket are given below. Use the range rule of thumb to estimate the standard deviation of all the $350$ apples in the basket. Compare the estimated standard deviation to the measured one of $5.12\text{g}$.

$145.3,149.2,152.0,154.5,157.3,158.1,161.2,163.5,166.0,167.8$

A random sample of $130$ male engineering students is obtained, and their heights are measured in $\text{inches}$ and in $\text{centimeters}$.

From the regression analysis, the predicted height in $\text{centimeters}$ for a student who is $70\text{ inches}$ tall is found to be $177.8\text{ cm}$. The sum of squared residuals from the regression is ${\text{42.25 cm}}^2$.

i. What is the value of the standard error of estimate (SE)?

ii. For a student whose height is $70\text{ inches}$, what is the $95\%$ prediction interval?

At a coffee shop, the mean expenditure per customer for $60$ customers is $\mathrm{\backslash (}10$, with a standard deviation of $\mathrm{\backslash )}2$. According to Chebyshev's Theorem, what is the minimum number of customers who spent between $\mathrm{\backslash (}6$ and $\mathrm{\backslash )}14$?

A research team records the systolic blood pressure (in units of millimeters of mercury) and resting heart rates (in units of beats per minute) of eight marathon runners. The blood pressures are $118$, $122$, $120$, $116$, $124$, $119$, $121$, and $117$. The heart rates are $58$, $62$, $60$, $56$, $64$, $59$, $61$, and $57$. Calculate the coefficient of variation for both blood pressure and heart rate. Which measurement is more variable relative to its mean?