Question 3 a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product. i. Define the variable of interest for this scenario. ii. What probability distribution do you think best describes the situation? Why? iii. Calculate the probability that exactly 9 will buy the product. iv. If 80 persons are introduced to the product, determine the number of person who are expected to buy the product. b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that i. Exactly 4 trains will pass in 30 minutes ii. less than 2 trains will pass in an hour
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 3
a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.
i. Define the variable of interest for this scenario.
ii. What
iii. Calculate the probability that exactly 9 will buy the product. iv. If 80 persons are introduced to the product, determine the number of person who are expected to buy the product.
b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that
i. Exactly 4 trains will pass in 30 minutes
ii. less than 2 trains will pass in an hour
Question 4
The length of a fully grown hibiscus plant is
i. Find the standard deviation σ.
ii. When plants are chosen for sale, those shorter than 30cm are rejected. Find the probability that a plant will be rejected.
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