Exam 26: Introduction to Statistics and Probability

In testing the thickness of a protective coating sprayed onto metal plates, there is a $88 \%$ probability that a single plate selected at random will pass inspection. What is the probability that of 15 plates sampled, 12 will pass inspection?

If you flip a coin and roll a die, what is the probability of obtaining a heads on the coin and a three or four on the die?

Find the probability that a card drawn from a deck will be either a four or a diamond.

A random survey of 80 students found they spent a mean of 21 hours in class per week with standard deviation of 3 hours per week. Find the $95 \%$ confidence interval for the population mean.

A random sample of 400 students found that $70 \%$ are currently enrolled in a mathematics course. Find the $95 \%$ confidence interval for the population proportion.

Find the area under the normal curve between the mean and 1.7 standard deviations. Use a table of area under the curve within $z$ standard deviations of the mean.

A particular beverage company states that the volumes of the bottles they produce are normally distributed with a mean of $2000 \mathrm{~mL}$ and a standard deviation of $10 \mathrm{~mL}$ . What is the probability that a randomly sampled bottle has a volume more than $2015 \mathrm{~mL}$ .

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 histogram, showing both absolute and relative frequencies.

The temperature of a metal casting set out to cool was recorded over time and the following data was found: Find the correlation coefficient and the least squares line.

Determine the quartiles and give the quartile range of the data: $211,226,228,240,256,292,310,376$ , $384,402,421$

The weight of a tray of $11 \mathrm{~mm}$ hex bolts and the number of bolts on the tray will have what correlation coefficient?

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 quartiles and find the quartile range of the lengths.

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 -Make a cumulative frequency distribution, showing (a) absolute frequency and (b) relative frequency.

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 median of the lengths.

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 sample variance and standard deviation of the lengths.

The proportion defective for samples of 200 calculators per day for 20 days as follows: Find the mean proportion defective and the values of the upper and lower control limits.

The distribution of grades on a certain test has a mean of 85.5 with a standard deviation of 11.2. There are 400 tests. Assuming that the grades are normally distributed, predict the number of students scoring between 75 and 95 . Use a table of area under the curve within $z$ standard deviations of the mean.

What is the arithmetic mean of the following sample of weights of Lake Ontario in kilograms. $1.7,2.1,1.3,0.7,1.7,1.5,1.3,2.0,1.9$

A single sample of size 64 drawn from a population is found to have a mean of 135 and a standard deviation of 8.3. Estimate the population mean with a confidence level of $68 \%$ .

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 mean of the lengths.