Practice Paper Statistics 1 (Edexcel International A Level Maths: Mechanics 2)

 Three events,,  and , are such that and  are independent and  and  are mutually exclusive. ,  , and the following two relations also hold: 

Using the above information, draw a Venn diagram to show the probabilities for events , and .

Find:

The histogram below shows the masses, in grams, of 80 apples.

Find estimates for the median, lower quartile and upper quartile.

Given that the lightest apple weighs 41 g and that the range of masses is 97 g, draw a box plot to show the distribution of the masses of the apples.

The ages, years, of 200 people attending a vaccination clinic in one day are summarised by the following:  = 7211  and  = 275 360.

Calculate the mean and standard deviation of the ages of the people attending the clinic that day.

One person chooses not to get the vaccine, so their data is discounted. The new mean is exactly 36.  Calculate the age of the person who left and the standard deviation of the remaining people.

The masses of turkeys can be modelled using a normal distribution with a mean of 4.7 kg and a variance of 1.9 kg².  Nicholas, a farmer, classes a turkey as ‘holiday ready’ if it weighs more than 5.5 kg.

A turkey is selected at random. Given that it is ‘holiday ready’, find the probability that it weighs less than 6 kg.

Nicholas takes a large sample of ‘holiday ready’ turkeys, estimate the median mass of the turkeys in his sample.

A machine is used to fill bags of potatoes for a supermarket chain. The weight, kg, of potatoes in the bags is normally distributed with mean 3 kg and standard deviation  kg. 

Given that 7% of the bags contain a weight of potatoes that is at least 50 g more than the mean, find:

.

Two of the bags of potatoes are chosen at random.

Find the probability that neither of the bags will contain less than 2.96 kg of potatoes.

A discrete random variable, , can take the values 1, 3, 5 or 7 and it has the cumulative distribution function  given in the table.

	1	3	5	7
	0.5	0.65	0.9	1

Find the value of:

.

Find the value of:

.

The random variable  has the probability function

Write down the value of .

Find the values of and .

Charlie is interested to find out if there is positive correlation between the number of letters in someone’s name, , and the time,  rounded to the nearest five seconds, it takes her six-year-old sister to correctly guess the spelling of the name.  She decides to test this by looking at a random sample of different names and timing how long it takes her sister to guess their spelling.

Letters,
Time,
Frequency

Given that , find the value of  and hence find the number of names in Charlie’s sample.

Charlie calculates the equation of the regression line of  on  to be  and the product moment correlation coefficient to be 0.84428 correct to 5 decimal places.

Find the value of and  each to 5 significant figures.