Q1: Exercises (Week 6) ‘Fit Camp’ is an intensive month-long programme of diet and exercise. Evidence shows that people who register for the programme and complete it see very satisfactory results. However, the regime is gruelling and experience dictates that 70% of people who register for the programme give up in the first 2 weeks. On a particular day, six people register for the programme. This can be thought of as a random sample. a) What is the probability that at least two of the six will give up in the first 2 weeks? b) What is the probability that at least two of the six will not give up in the first 2 weeks? Q2: Automobile Association records indicate that, on average, 3.2 breakdowns per day occur on a particular section of a UK motorway during the morning rush hour. Assume that the distribution is Poisson. a) Find the probability that on any given day there will be fewer than two breakdowns on this section of motorway during the morning rush hour. b) Find the probability that on any given day there will be more than four breakdowns on this section of motorway during the morning rush hour. Q3: (Taken from ‘Simple Statistics’ by Frances Clegg) Using a Normal distribution table, translate the following z scores into percentage areas under the curve: Hint: We are looking for the area to the left of these values (a) -2.43 (b) -1.88 (c) -0.36 (d) 0 (e) +1.47 Q4: A research study estimates that the amount it costs to raise a child (up to the age of 18) is Normally distributed with a mean of £500,000 and standard deviation £50,000. a) What is the probability that the cost of raising a child (as defined above) will be between £460,000 and £540,000? b) The probability is 0.2 that raising a child will cost less than how much? c) Find the shortest range such that the probability is 0.95 that the cost of raising a child will fall in this range. Q5: Given a random sample of size n = 900 from a Binomial probability distribution with p = 0.5: a) Find the probability that the number of successes is greater than 500 b) Find the probability that the number of successes is less than 430 c) With probability 0.10 the number of successes is less than how many?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Q1:
Exercises (Week 6)
‘Fit Camp’ is an intensive month-long programme of diet and exercise. Evidence shows that people who register for the programme and complete it see very satisfactory results. However, the regime is gruelling and experience dictates that 70% of people who register for the programme give up in the first 2 weeks. On a particular day, six people register for the programme. This can be thought of as a random sample.
-
a) What is the
probability that at least two of the six will give up in the first 2 weeks? -
b) What is the probability that at least two of the six will not give up in the first 2 weeks?
Q2:
Automobile Association records indicate that, on average, 3.2 breakdowns per day occur on a particular section of a UK motorway during the morning rush hour. Assume that the distribution is Poisson.
-
a) Find the probability that on any given day there will be fewer than two breakdowns on this section of motorway during the morning rush hour.
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b) Find the probability that on any given day there will be more than four breakdowns on this section of motorway during the morning rush hour.
Q3: (Taken from ‘Simple Statistics’ by Frances Clegg)
Using a Normal distribution table, translate the following z scores into percentage areas under the curve:
Hint: We are looking for the area to the left of these values
(a) -2.43 (b) -1.88 (c) -0.36 (d) 0 (e) +1.47
Q4:
A research study estimates that the amount it costs to raise a child (up to the age of 18) is
-
a) What is the probability that the cost of raising a child (as defined above) will be between £460,000 and £540,000?
-
b) The probability is 0.2 that raising a child will cost less than how much?
-
c) Find the shortest
range such that the probability is 0.95 that the cost of raising a childwill fall in this range.
Q5:
Given a random sample of size n = 900 from a Binomial probability distribution with p = 0.5:
-
a) Find the probability that the number of successes is greater than 500
-
b) Find the probability that the number of successes is less than 430
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c) With probability 0.10 the number of successes is less than how many?
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