Question 1 of 8descriptive statistics
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A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5,…
A student travels to school by bus, car, or on foot with probabilities \frac{1}{6}, \frac{1}{3}, and \frac{1}{2} respectively. The…
According to the Central Limit Theorem, for a sufficiently large sample size n drawn from any population with mean \mu and variance…
The volume of dish washing liquid in a satchet is normally distributed with mean 400 ml and standard deviation 45 ml. The volume of fabric…
A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is…
A student travels to school by bus, car, or on foot with probabilities \frac{1}{6}, \frac{1}{3}, and \frac{1}{2} respectively. The…
120 bags of mealie-meal have mean mass 750g and standard deviation 3.9g. What is the standard error of the mean, correct to 3 decimal…
A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than…
A head of school can contact parents by e-mail, letter or cellphone with probabilities 0.4, 0.1 and 0.5 respectively, using only one…
The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the…
120 bags of mealie-meal have mean mass 750g and standard deviation 3.9g. Using a 95% confidence interval with z = 1.96, what is the upper…
A machine packs washing powder into packets that are normally distributed with mean 2 kg and standard deviation 0.039 kg. Find the…
A head of school contacts parents by e-mail, letter or cellphone with probabilities 0.4, 0.1 and 0.5 respectively. The probability parents…
The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the…
An ice cream vendor's sales are 40% chocolate, 35% vanilla and 25% peach. The probability of a cone sale is 0.80 for chocolate, 0.60 for…
A continuous random variable X has probability density function f(x) = \dfrac{3}{8}x^2 for 0 \leq x \leq 2. Find the value of the…
Which of the following is not one of the four traditional components of a time series?
The times to the nearest minute taken by 12 students to complete a task are 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44, giving Q1 = 42,…
Which of the following is an advantage of using telephone interviews as a way of collecting data?
A continuous random variable X has probability density function f(x) = \dfrac{x}{12} for 0 \le x < 3, f(x) = k(x-8) for 3 \le x \le 8, and…
The volume of dish washing liquid in satchets is normally distributed with mean 400 ml and standard deviation 45 ml, independent of the…
When selecting a number of objects from a set, which condition makes the selection a permutation rather than a combination?
A continuous random variable X has probability density function f(x) = \dfrac{x}{12} for 0 \le x < 3 and f(x) = -\dfrac{1}{20}(x-8) for 3…
A new detergent is made by mixing the contents of 1 satchet of dish washing liquid, mean volume 400 ml, with 2 bottles of fabric softener,…
What is the formula, in terms of n and r, for the number of permutations of r objects chosen from n distinct objects?
A continuous random variable X has probability density function f(x) = \dfrac{x}{12} for 0 \le x < 3 and f(x) = -\dfrac{1}{20}(x-8) for 3…
A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than…
Whenever there is a power-cut, a school is equally likely (probability 1/3 each) to switch on one of its 3 generators A, B or C. The…
A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample…
Packets of washing powder have weights normally distributed with mean 2 kg and standard deviation 0,039 kg. What proportion of packets…
Using the same power-cut scenario (each generator equally likely to be switched on with probability 1/3; independent breakdown…
In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0…
A continuous random variable X has probability density function f(x) = (3/8)x^2 for 0 <= x <= 2. What is the cumulative distribution…
An unbiased die with faces marked 1, 2, 2, 3, 3, 3 is rolled twice. If X is the total score on the two rolls, what is P(X = 4), as a…
In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0…
A continuous random variable X has cumulative distribution function F(x) = x^3/8 for 0 <= x <= 2. What is the median m of X? Give your…
A man pulls a crate of weight 20 N along a rough horizontal floor using a string inclined at 60° to the horizontal. The crate is in…
Continuing the crate scenario (weight 20 N, pulling force 4 N at 60° to the horizontal, normal reaction R=20-2\sqrt3 N, limiting…
A manufacturing plant uses three machines, A, B and C, in its production process. The total daily output contributions of machines A, B and…
The diameters of 25 steel rods have a sample mean of 0.980 cm and a standard deviation of 0.015 cm. Assuming the diameters are normally…
A stem-and-leaf diagram of pocket money (in dollars) received by a group of girls is given below, with key 3|30 = \$3.30: Stem 0: 50 50 50…
An experiment has only two possible outcomes. The first outcome occurs with probability p and the second outcome occurs with probability…
A manufacturing plant uses three machines, A, B and C, contributing 40%, 45% and 15% of daily output respectively, with defect rates of 4%,…
The masses (g) of 24 sweets, read off a stem-and-leaf diagram and placed in ascending order, are: 0.72, 0.73, 0.79, 0.80, 0.88, 0.91, 0.91,…
Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550,…
A survey in a city shows that the probability a person is in favour of capital punishment is 0.55 and the probability a person is against…
A factory produces two types of nut and bolt with normally distributed masses. Type A bolts have mean mass 20.5 g and Type A nuts have mean…
Using the same 24 sweet masses (g) 0.72, 0.73, 0.79, 0.80, 0.88, 0.91, 0.91, 0.94, 0.98, 0.99, 1.01, 1.03, 1.06, 1.08, 1.13, 1.13, 1.13,…
A school's lower sixth intake is 55% from its own O-level pupils and 45% from other schools. Of those who did O-level elsewhere, 90% pass…
The continuous random variable X has probability density function f(x)=\frac{1}{28}(6x-4) for 2\le x\le4 (and 0 otherwise). Find E(X),…
A factory produces two types of nut and bolt with independent, normally distributed masses, each with standard deviation 0.2 g. Type A…
A sweet with mass greater than 1.2 g is classified as large. From the 24 masses (g) 0.72, 0.73, 0.79, 0.80, 0.88, 0.91, 0.91, 0.94, 0.98,…
Using the same school (55% own O-level pupils, 45% from elsewhere; pass rates 70% and 90% respectively, overall pass probability 0.79),…
The table below shows the masses of 200 students measured to the nearest kg. | Mass (kg) | Number of students | | --- | --- | | 46-50 | 20…