Math AI Quiz (Trig & Probability Distributions)

Find the measure of the smallest angle in a triangle that has side lengths 6, 8, and 12. Round to 1 decimal place and do not include units.

Find the area of an equilateral triangle with side length 10. Round to 1 decimal place and do not include units.

Which one of the following is a discrete random variable?

• Daler's height

• Daler's weight

• The time it takes Daler to run the 110 m hurdles

• The amount of Daler's brothers and sisters

A group of IB students' mock exam test scores are normally distributed with mean 56, and standard deviation 8. What is the probability that a student scored less than 56?

• 50%

• 56%

• 28%

• 18.7%

In a multiple choice test there are 30 questions. Each question has 4 choices, one of which is correct. Cesar, who knows nothing about the subject, guesses each answer at random. Let X be the number of questions that Jerry has guessed correctly. What is the standard deviation of X? (Round to 3 sf)

A random variable X is normally distributed with mean 40, and standard deviation unknown. The diagram shows the normal curve for X. The area of the shaded region is 0.28. What is

 $P\left(40\le X\le48\right)$  ?

• 50%

• 22%

• 68%

• 99.5%

What is the measure of angle A? Round to 3sf, and do not include units in your answer.

The height of a group of 80 people is known to be normally distributed with mean 180cm, and standard deviation 8cm. Approximately how many people do we expect to be 1 standard deviation below the mean? Round your answer to the nearest whole number.

The results of a test are known to be normally distributed with mean 75 and standard deviation 7. We know that 10% of the students scored above X.

What is X, to the nearest integer?

To approximate the length of a marsh, a surveyor walks 425 meters from point A to point B. Then the surveyor turns 65º and walks 300 meters to point C. Approximate the length of the marsh, AC. Round to 3 sf. Do not include units.