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1333 quizzes
A park ranger groups the lengths of 40 fallen branches, in classes of width 10 centimetres: 0 to 10 with frequency 3, 10 to 20 with 9, 20 to 30 with 14, 30 to 40 with 10 and 40 to 50 with 4. What is the median length, to two decimal places? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A technician measures the voltage of a battery five times and gets 10, 13, 14, 16 and 17 volts. She treats the readings as a random sample of all possible readings and wants an estimate of the variance of the voltage. What is the sample variance? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
Ten readings have a mean of 30 and a standard deviation of 5. One reading of 24 is found to be wrong, and the correct reading is 34. What is the variance of the corrected readings? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
The figure shows box plots of the marks of two classes, P and Q, on the same scale. Class P has the box from 40 to 60 with the median at 50. Class Q has the box from 45 to 85 with the median at 70. Which statement about the two classes is correct? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
For a data set, the regression coefficient of y on x is -2 and the regression coefficient of x on y is -0.125. What is the correlation coefficient? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
The figure shows the number of cups of hot drinks sold by a cafe against the noon temperature on eight days. The line of best fit passes through the point of the means, (24, 50), and its slope is -2.5 cups for each degree. What number of cups does the line predict for a noon temperature of 30 °C? New
High School (11–12) · Statistics
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
Let X ∼ B(9, 0.3). Which statement about the most likely value of X is true? New
High School (11–12) · Random Variables and Probability Distributions
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A fair coin is tossed 100 times, and X is the number of heads. A student uses the normal approximation with a continuity correction to estimate P(X ≤ 45). A table gives Φ(0.8) = 0.7881, Φ(0.9) = 0.8159, Φ(1.0) = 0.8413 and Φ(1.1) = 0.8643. Which value does she get? New
High School (11–12) · Random Variables and Probability Distributions
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A game counts the heads X in 10 tosses of a fair coin and pays X² - 10 rupees. A player pays no entry fee. What is the expected payout, in rupees? New
High School (11–12) · Random Variables and Probability Distributions
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Advanced
Ananya draws cards one at a time from a well-shuffled pack of 52 cards, without replacement, until an ace appears. What is the probability that the first ace appears on the third card? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A signal passes through three relays in a chain, and it gets through only if all three work. Each relay works independently with probability 0.9. To improve the link, an identical second chain of three relays is built beside the first. The signal gets through if at least one chain works. What is the probability that the signal gets through? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
In a survey, 80% of residents own a bicycle (event A) and 70% own a scooter (event B). Among the bicycle owners, what is the smallest possible percentage who also own a scooter? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Advanced
A laboratory screens samples for a contaminant that is present in 5% of them. The screen is positive for 90% of the contaminated samples and for 5% of the clean samples. One sample is screened twice, with independent results, and both are positive. What is the probability that the sample is contaminated? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A visitor knocks at the door of a house with two children. One of the two children, chosen at random, opens the door, and it is a girl. Each child is equally likely to be a girl or a boy, independently of the other. What is the probability that both children are girls? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
A game show has three doors, with a prize behind one. A contestant picks door 1. The host does not know where the prize is. He opens door 3 at random, and it happens to show no prize. What is the probability that the prize is behind door 2? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Hard
Three cards are in a hat. One card is red on both sides. One card is white on both sides. The third card is red on one side and white on the other. A card is drawn at random and put on a table. The side facing up is red. What is the probability that the side facing down is also red? New
High School (11–12) · Conditional Probability and Bayes' Theorem
APA-LevelIB+23APA-LevelIB
StemPy LabStemPy Lab
Advanced
A line makes an angle of 45° with the x-axis and an angle of 45° with the y-axis. What angle does it make with the z-axis? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
The direction ratios of a line are (a, b, c). A student multiplies all three by -2 and works out new direction cosines. How are the new direction cosines related to the old ones (l, m, n)? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
The figure shows a cube of edge 1 unit with a corner O at the origin. The red line is the body diagonal OG and the blue edge OA lies along the x-axis. What is the angle between OG and OA? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
Two pipes follow the lines through (1, -1, 0) with direction ratios (1, 2, -1) and through (1, 0, -3) with direction ratios (2, k, 1). The pipes must meet at a joint. For which value of k is this possible? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
The shortest distance between two lines that are not parallel is found to be 0. What does this tell you about the two lines? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
The figure shows a blue line parallel to the x-axis through (0, 1, 1) and a red line parallel to the y-axis through (-1, -3, 3), with lengths in metres. A cable car designer needs the shortest distance between the two lines. What is it? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
Two parallel glass sheets lie in the planes 2x - y + 2z = 1 and 4x - 2y + 4z = -10, with lengths in metres. What is the distance between the sheets? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
Two sloping steel plates in a bridge frame lie in the planes x + 2y - z = 1 and 2x - y + z = 3. Where they meet, a weld seam runs along a straight line. A welder needs a vector that points along the seam. Which vector does she use? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
The figure shows the part of a plane in the first octant. It meets the axes at A(6, 0, 0), B(0, 3, 0) and C(0, 0, 2), with lengths in metres. What is the shortest distance from the origin to the plane? New
High School (11–12) · Three-Dimensional Geometry
A-LevelIBAEEE (Amrita)+23A-LevelIB
StemPy LabStemPy Lab
Hard
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