Mean and Standard Deviation of Probability Distributions

Which of the following is a discrete numerical variable?

• The number of students in a class.

• The height of a person.

• The weight of a car.

• Distance between two cities.

Which one of the following variables is a continuous variable?

• The height of Year 12 students in a high school.

• The number of people on a bus.

• The score out of 90 for a test.

• The number of computers in a computer room in a school.

Which of the following could be the population of interest for a statistician to survey and draw a conclusion.

• The people that live in a city.

• The people that live in a certain ward of a city.

• The people that live on a certain street in a city.

• All of these.

Clara discovers that the height of sunflowers in a farmer's field is normally distributed with mean 130 cm and standard deviation 15 cm.

Using the familiar portions of 1, 2, 3 standard deviations, approximately what proportion of the sunflowers will be taller than 160 cm?

• 10%

• 5%

• 2.5%

• 25%

The lifespan of radios is normally distributed with a mean of 15.2 years and a standard deviation of 5 years. 5% of the radios last longer than k years. Find the value of k.

• ≈23.4 years

• ≈19.8 years

• ≈36.1 years

• ≈15.2 years

In the city of Longskank, the mean adult weight is 62kg and the standard deviation is 10kg. Assuming that the weight of adult males is normally distributed, find the probability that an adult chosen at random weighs between 62kg and 85kg?

• 0.489

• 0.511

• 0.326

• 0.296

In the city of Longskank, the mean adult weight is 62kg and the standard deviation is 10kg. Assuming that the weight of adult males is normally distributed, find the probability that an adult chosen at random weighs more than 85kg.

• 0.0107

• 0.306

• 0.0654

• 0.211

LEVEL ONE: Decide which method you’d use to START the question.

The mass of an adult male is normally distributed with a mean of 79.4 kg and a standard deviation of 20kg. Find the probability that a randomly selected adult has a mass of at least 65kg.

• venn diagram

• tree diagram

• binomial probability

• normal cdf

• z-score formula

LEVEL ONE: Decide which method you’d use to START the question.

Miss Coppola is measuring earthworms during a rain storm. She finds that they are normally distributed with a mean of 138 mm and a standard deviation of 40 mm. Calculate the proportion of earthworms which are between 100 mm and 200 mm in length.

• venn diagram

• tree diagram

• binomial probability

• normal cdf

• z-score formula

Emma is playing a spinning game using the spinner shown. She gets one spin and needs green to win. What's probability that she will NOT win?

• .25
• .75
• .70
• 40