Warm Up
Normal Distribution
Binomial Distribution
Statistics
Probability
100
Find the range of the values in the given set of data
{22, 48, 52, 96, 77, 39}
What is 74?
100
The random variable X is normally distributed with a mean of 100. The following diagram shows the normal curve for X.
Let R be the shaded region under the curve, to the right of 107. The area of R is 0.24.
Write down P(X>107).
What is 0.24?
100
A factory makes lamps. The probability that a lamp is defective is 0.05. A random sample of 30 lamps is tested.
Find the probability that there is at least one defective lamp in the sample.
What is 0.785?
100
A school collects cans for recycling to raise money. Sam’s class has 20 students.
The number of cans collected by each student in Sam’s class is shown in the following stem and leaf diagram.
Find the median number of cans collected.
What is 38?
100
Let A and B be independent events, where P(A)=0.6 and P(B)=x. Write down an expression for P(A∩B).
What is P(A∩B)=P(A)×P(B)(=0.6x)?
200
Find the mean, median, and mode of the values in the given set of data
{3, 2, 7, 4, 3, 5, 6, 4, 8, 3}
What is 4.5, 4, and 3?
200
A random variable X is distributed normally with mean 450 and standard deviation 20.
Find P(X≤475) .
What is 0.894?
200
A factory makes switches. The probability that a switch is defective is 0.04. The factory tests a random sample of 100 switches.
Find the probability that there are exactly six defective switches in the sample.
What is 0.105?
200
The following table shows the average number of hours per day spent watching television by seven mothers and each mother’s youngest child.
The relationship can be modelled by the regression line with equation y=ax+b.
Find the correlation coefficient, the value of a, and the value of b.
What is r=0.947, a=0.501, b=0.804?
200
The following Venn diagram shows the events A and B, where P(A)=0.4, P(A∪B)=0.8 and P(A∩B)=0.1. The values p and q are probabilities.
Find the value of q and p.
What is 0.1 and 0.3?
300
There are 10 items in a data set. The sum of the items is 60. The variance of this data set is 3. Each value in the set is multiplied by 4.
Find the value of the original mean and the new mean.
What is 6 and 24?
300
The heights of a group of seven-year-old children are normally distributed with mean 117 cm and standard deviation 5 cm. A child is chosen at random from the group.
The probability that this child is shorter than k cm is 0.65. Find the value of k.
What is 119?
300
A company produces a large number of water containers. Each container has two parts, a bottle and a cap. The bottles and caps are tested to check that they are not defective.
A cap has a probability of 0.012 of being defective. A random sample of 10 caps is selected for inspection.
Find the probability that exactly one cap in the sample will be defective.
What is 0.108?
300
The histogram below shows the time T seconds taken by 93 children to solve a puzzle.
A child is selected at random. Find the probability that the child takes less than 95 seconds to solve the puzzle.
What is 0.817?
300
The following table shows the probability distribution of a discrete random variable X.
Find E(X). (Hint: find k first)
What is 3.3?
400
A data set has n items. The sum of the items is 800 and the mean is 20. The standard deviation of this data set is 3. Each value in the set is multiplied by 10.
Find the value of the new mean and the new variance.
What is 200 and 900?
400
A random variable X is normally distributed with μ=150 and σ=10 .
Find the interquartile range of X .
What is 13.5?
400
Jan plays a game where she tosses two fair six-sided dice. She wins a prize if the sum of her scores is 5.
Jan tosses the two dice 8 times. Find the probability that she wins 3 prizes.
What is 0.0426?
400
The cumulative frequency curve below represents the marks obtained by 100 students.
Find the median mark and the interquartile range.
What is 56 and 30?
400
Bill and Andrea play two games of tennis. The probability that Bill wins the first game is 4/5. If Bill wins the first game, the probability that he wins the second game is 5/6. If Bill loses the first game, the probability that he wins the second game is 2/3.
Find the probability that Bill wins the first game and Andrea wins the second game.
What is 2/15?
500
A letter is chosen at random from the 26-letter English alphabet. Find the probability that the letter is in the word MATHEMATICS.
What is 4/13?
500
The masses of watermelons grown on a farm are normally distributed with a mean of 10 kg.The watermelons are classified as small, medium or large. The following table shows the percentages of small, medium and large watermelons grown on the farm.
All the medium and large watermelons are delivered to a grocer.
The grocer sells all the medium watermelons for $1.75 each, and all the large watermelons for $3.00 each. His costs on this delivery are $300, and his total profit is $150. Find the number of watermelons in the delivery.
What is 200?
500
Two fair 4-sided dice, one red and one green, are thrown. For each die, the faces are labelled 1, 2, 3, 4. The score for each die is the number which lands face down.
Fred plays a game. He throws two fair 4-sided dice four times. He wins a prize if the sum is 5 on three or more throws.
Find the probability that Fred wins a prize.
What is 0.0508?
500
The following box-and-whisker plot shows the number of text messages sent by students in a school on a particular day.
One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.
What is k=22?
500
A company uses two machines, A and B, to make boxes. Machine A makes 60% of the boxes. 80% of the boxes made by machine A pass inspection. 90% of the boxes made by machine B pass inspection.A box is selected at random.
The company would like the probability that a box passes inspection to be 0.87.
Find the percentage of boxes that should be made by machine B to achieve this.
What is 70%?