(d) Will this Olympic swimmer be offered a contract to endorse the sports deodorant by the advertising agency? Use the confidence interval from (c) in your reasoning. (e) A tennis player has recognition rate of 70% in the general population. What is the probability that less than 65% of a random sample of 420 people would recognise this tennis player?
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.
Question resubmitted for solutions to parts (d) and (e):
An advertising agency won’t sign an athlete for product endorsement unless it is sure that the athlete is recognised by more than 25% of its target audience. The agency always conducts a poll to investigate the level of recognition of the athlete before offering a contract.
(b) (already answered, for reference only) The target audience for a new sports deodorant is 13 to 19 year-old girls who play sport. From a sample of 800 teenagers from this population a total of 216 indicated that they recognised a particular Olympic swimmer. What are the population and random variable under consideration in this case?
(c) (already answered, for reference only) Calculate a 95% confidence interval for the population level of recognition for this swimmer. Be sure to outline any necessary conditions for validity of this confidence interval.
(d) Will this Olympic swimmer be offered a contract to endorse the sports deodorant by the advertising agency? Use the confidence interval from (c) in your reasoning.
(e) A tennis player has recognition rate of 70% in the general population. What is the probability that less than 65% of a random sample of 420 people would recognise this tennis player?
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