Day 1: Sampling Concepts and Summarizing Data
A shop owner wants to find out what proportion of the scarves she sells are bought by women. She thinks that this may depend on the colour of scarves, so she records the gender of the customers who bought the first 10 of each color of scarf.
Give the name of this type of sampling?
Quota sampling
A fair eight-sided dice has sides numbered 1, 1, 1, 2, 2, 3, 4, 5. The dice is rolled 30 times. Estimate the number of times it will land on a 2.
1/4
Two cards are selected at random from a standard pack of 52 cards.
Find the probability that both cards are hearts.
1/17
The heights of trees in a forest are modelled by a normal distribution with mean 17.2 m and standard deviation 6.3 m. Find the probability that a randomly selected tree has a height between 15m and 20m.
0.308
For the set of data: 3, 6, 1, 3, 2, 11, 3, 6, 8, 4, 5
Find the median
4
A bag contains 12 green balls and 18 yellow balls. Two balls are taken out at random. Find the probability that they are different colors.
0.496
A multiple-choice test consists of 25 questions, each with five possible answers. Daniel guesses answers at random.
Find the probability that Daniel gets fewer than 10 correct answers.
0.983
The daily amount of screen time among teenagers can be modelled by a normal distribution with mean 4.2 hours and standard deviation 1.3 hours.
What percentage of teenagers get more than 6 hours of screen time per day?
0.0831
The mean of the values 2x, x +1, 3x, 4x-3, x and x-1 is 10.5.
Find the variance of the values?
30.9
Three fair six-sided dice are thrown and the score is the sum of the three outcomes. Find the probability that the score is equal to 5.
1/36
A game stall offers the following game: You toss three fair coins. You receive the number of dollars equal to the number of tails. How much should the stall charge for one game in order to make the game fair?
Among 17-year-olds, the times taken to run 100 m are normally distributed with mean 14.3 s and variance 2.2 s2 . In a large competition, the top 15% of participants will qualify for the next round. Estimate the required qualifying time.
12.8 seconds
Lucy must sit five papers for an exam. In order to pass her Diploma, she must score an average of at least 60 marks. In the first four papers Lucy scored 72, 55, 63 and 48 marks. How many marks does she need in the final paper in order to pass her Diploma?
62 marks
Events A and B satisfy: P(A) = 0.7, P(A ∪ B) = 0.9 and P(B′) = 0.3. Find P(A ∩ B).
0.5
An archer has the probability of 0.7 of hitting the target. A round of a competition consists of 10 shots.
A competition consists of five rounds. Find the probability that the archer hits the target at least seven times in at least three rounds of the competition.
0.765
Given that Y ~ N(13.2, 5.1^2 ) , find the value of c such that P(c<Y<17.3) =0.14
15.2
Juan needs to take six different tests as part of his job application. Each test is scored out of the same total number of marks. He needs an average of at least 70% in order to be invited for an interview. After the first four tests his average is 68%. What average score does he need in the final two tests?
74%
A computer scientist uses a method called Monte Carlo sampling to estimate the value of π. He uses a random number generator to generate 100 points at random inside a 1 by 1 square. Of these points, 78 are inside the largest circle which can be drawn in the square. What would be the estimate of π she would form on the basis of this sample?
3.12
A random variable X follows binomial distribution B (n, p). It is known that the mean of X is 36 and the standard deviation of X is 3. Find the probability that X takes its mean value.
0.132
A farmer has chickens that produce eggs with masses that are normally distributed with mean 60 g and standard deviation 5 g. Eggs with a mass less than 53 g cannot be sold. Eggs with a mass between 53 g and 63 g are sold for 12 cents and eggs with a mass above 63 g are sold for 16 cents. If the farmer’s hens produce 6000 eggs each week, what is the farmer’s expected income from the eggs.
Each egg is 12.1 cents
Total is $728