Probability and Statistics

Using Maximum Likelihood Estimation (MLE), determine the optimal mean and standard deviation for a normal distribution that best fits the measured weights of a group of mice.

Calculate the mean, median, mode, and range for a given set of numbers: 7, 5.29, 4, and another number resulting in a range of 12.

Find the mean (average), median, and mode of data set {1, 8, 3, 2, 6}.

Calculate the mean age of a family with ages totaling 222 years for 6 members.

Given a data set {1, 2, 3, 4}, determine the median.

Using a dataset of monthly guitar sales totaling 108 over 12 months, find the mean, median, and mode.

What’s the probability of rolling snake eyes?

What’s the probability of flipping heads three times in a row?

What’s the probability that you’ll draw an ace, hold onto it, and then draw a king?

Suppose that we want to find out the probability of first drawing a green marble and then a blue marble out of a bag of 12 marbles. There are three green marbles, four blue marbles, and five red marbles. Find the probability using the multiplication rule of probability.

Scores on an exam are normally distributed with a mean of 65 and a standard deviation of 9. We want to find the percent of scores satisfying a) $x < 54$, b) $x \ge 80$, c) $70 < x < 86$.

You love pizza, and your local pizza shop claims that their large is at least 16 inches or it's free. Over your expansive pizza eating career, you've found that their pizzas are normally distributed in size with a mean of 16.3 inches and a standard deviation of 0.2 inches.

Now you want to know: What is the probability of getting a free pizza? Also, what's the probability of getting a pizza that's over 16.5 inches? And, what's the probability of getting a pizza that's between 15.95 inches and 16.63 inches?

A survey showed that the average male baby in the UK weighs 7 pounds 12 ounces at birth. A midwife in a Birmingham hospital suspects the birth weight may have increased in recent years and collects data to find out. Define the null and alternative hypotheses.

The vending machine should dispense bottles of water expected to contain 500 ml. A service engineer suspects that the actual amount in each bottle is less.

Define the null and alternative hypotheses.

There is no difference in birth weight between babies born in Birmingham hospitals ($\mu_B$) and babies born in Nottingham hospitals ($\mu_N$). However, the alternative hypothesis is that there is a difference. Define the null and alternative hypotheses.

Company XYZ manufactures calculators with an average mass of 450 grams. An engineer believes that average weight to be different and decides to calculate the average mass of 50 calculators. State the null and alternative hypotheses.

The teachers in a school believe that at least 80 percent of students will complete high school. A student disagrees with this value and decides to conduct a test. State the null and alternative hypotheses.

A teacher wishes to test if the average GPA of students in the high school is different from 2.7. State the null and alternative hypotheses.

The percentage of residents who own a vehicle in Town XYZ is no more than 75 percent. A researcher disagrees with the value and decides to survey 100 residents asking them if they own a vehicle. State the null and alternative hypotheses.