Exam 26: Introduction to Statistics and Probability

The amount of hours spent on homework and studying per week for a sample of 30 random students is given below: 3 5 6 6 7 7 7 7 8 8 9 10 10 12 13 14 14 14 15 15 17 19 20 20 21 21 24 27 28 30 (a) Find the mean. (b) Find the median. (c) Find the mode. (d) Find the range. (e) Find the standard deviation to three significant digits.

The heights (in centimeters) of 35 students at Hatfield College are given below: $157.5, 142.2, 172.7, 165.1, 165.1, 177.8, 180.3, 165.1, 167.6, 180.3,\\162.6, 182.9, 147.3, 152.4, 157.5, 162.6, 172.7, 185.4, 155.0, 167.6,\\170.2, 177.8, 170.2, 175.3, 167.6, 190.5, 175.3, 160.0, 172.7, 160.3,\\165.1, 172.7, 175.3, 165.1, 162.6$ (a) Determine the range of the data. (b) Make a frequency distribution using class widths of $8 \mathrm{~cm}$ . Show both absolute and relative frequencies. (c) Draw a frequency polygon showing both absolute and relative frequencies. (d) Make a cumulative frequency distribution. Show both absolute and relative frequencies. (e) Find the mean. (f) Give the 5-number summary (minimum, $1^{\text {st }}$ quartile, median, $3^{\text {rd }}$ quartile, maximum). (g) Find the standard deviation. Assume that the heights are a sample drawn from a larger population.

In "old school" Dungeons and Dragons game, you might find that for your character to defend against an attack, you have to roll 17 or higher on a 20 -sided die. What is the probability of defending against three attacks in a row?

For the table in problem 60 , find the average range $\bar{R}$ , and determine the upper and lower control limits for the range.

Five pieces of tubing are taken from a production line each day for 20 days and the lengths are measured. Their lengths, in $\mathrm{cm}$ , are as follows: Find the values of the central line and upper and lower control limits for the mean.

Define the following type of data as continuous, discrete, or categorical: The time it takes to drive from one city to another.

The amount of texts sent per day for a sample of 10 random people is given below: 5 10 25 25 40 50 60 75 100 120 (a) Find the mean. (b) Find the median. (c) Find the mode. (d) Find the range. (e) Find the standard deviation to three significant digits.

On a test given to 150 students, the mean grade was 74.2 with a standard deviation of 9.8. Assuming a normal distribution, estimate the number of $B$ grades (between 80 and 90).

In a normal distribution, the mean is 85 , and the standard deviation is 12 . For a single value, a z-score is 1.3. What is the value?

A factory kept track of its defectives (from random samples of 400 ) for 10 days and the following data was found: Find the values for the central line, and determine the upper and lower control limits.

A local refinery produces an amount of oil that is normally distributed with a mean of 250000 barrels per day with a standard deviation of 25000 barrels per day. What is the probability that the refinery will produce more than 300000 barrels on a given day?

Use the information below for questions. The average monthly rainfall (cm) in several cities in a certain province are: 11.3 29.6 16.3 31.4 29.2 14.5 16.9 25.8 21.3 32.7 15.3 13.5 25.2 22.5 18.6 14.3 26.9 22.9 -Draw a cumulative frequency polygon, showing both absolute and relative frequencies.

The speeds of 180 randomly chosen cars passing a certain point on a highway were measured. The mean was found to be $104.2 \mathrm{~km} / \mathrm{h}$ and their standard deviation was $6.1 \mathrm{~km} / \mathrm{h}$ . Estimate the mean speed of the entire population of cars with a confidence level of $95 \%$ .

Find the area under the normal curve between 1.2 standard deviations on both sides of the mean.

Consider the below set of lengths for questions: 123 422 566 329 247 296 245 522 362 593 229 475 357 227 489 326 -Find the mode of the lengths.

A factory claims a $4 \%$ defective rate on items produced. If a quality control engineer samples 25 items, what is the probability that 3 are defective? Express your answer to four decimal places.

Define the following type of data as continuous, discrete, or categorical: The number of times a person dines out at a restaurant (per month).

A random survey of 100 people asking the number of cups of coffee they drank per week found a mean of 8 with standard deviation of 2.5 . Find the $68 \%$ confidence interval for the population mean.

Use the information below for questions. The average monthly rainfall (cm) in several cities in a certain province are: 11.3 29.6 16.3 31.4 29.2 14.5 16.9 25.8 21.3 32.7 15.3 13.5 25.2 22.5 18.6 14.3 26.9 22.9 -Draw a frequency polygon showing both absolute and relative frequencies.

What is the probability of a sum of 6 when rolling 3 standard six sided dice?