It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
It was discovered that the sizing of some shirts was labelled incorrectly.
(i) Give two reasons why it would be necessary to examine a sample of the shirts produced
rather than examine the entire weekly production.
(ii) State two differences between a cluster sample and a stratified random sample in this situation.
(iii) Using the stratified random sampling technique, calculate the number of medium shirts
that will be selected if we require a sample of 375 shirts.
(iv)State one advantage of using stratified random method for collecting this sample.
b) Determine the level of measurement that describes the following
(i) The size of the shirt that a customer purchase
(ii) The total amount paid by the customer
(iii) The address of the factory that manufactures the shirts
c) A machine packages shirt in bags with a mean weight of 3 kg. A random sample of 20 bags
has a mean weight of 3.05 kg with a standard deviation of 0.05kg, From the data given, state the
value of a
(i) parameter
(ii) statistic
![Assessment #1: Problem Sets/Worksheet (Units 1, 2 & 3)
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Question 1
112 marks]
The following table shows the number of shirts by sizes that are manufactured in a factory on a
particular week:
Extra Small
390
Extra Large
440
Medium
Large
680
Small
470
520
a) It was discovered that the sizing of some shirts was labelled incorrectly.
(i) Give two reasons why it would be necessary to examine a sample of the shirts produced
rather than examine the entire weekly production.
(ii) State two differences between a cluster sample and a stratified random sample in this
situation.
[2]
[2]
(iii) Using the stratified random sampling technique, calculate the number of medium shirts
that will be selected if we require a sample of 375 shirts.
(iv)State one advantage of using stratified random method for collecting this sample. [1]
[2]
b) Determine the level of measurement that describes the following
(1) The size of the shirt that a customer purchase
(ii) The total amount paid by the customer
(ii) The address of the factory that manufactures the shirts
c) A machine packages shirt in bags with a mean weight of 3 kg. A random sample of 20 bags
has a mean weight of 3.05 kg with a standard deviation of 0.05kg, From the data given, state the
[3]
value of a
(i) parameter
(ii) statistic
[1]
[1]
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