113 7.7 Topic 7: The Normal Distribution 00. Suppose a population is unimodal and symmetric with mean 55 and standard deviation 7. Use Figure 7.11 to aid in answering the following questions. (a) Approximately what percent of observations are below 34? (b) Approximately what percent of observations are above 55? (c) Approximately what percent of observations are between 41 and 62? (d) Approximately what percent of observations are above 48? Figure 7.11: Depiction of the Empirical Rule for X N(55, 7) X: 34 41 48 55 62 69 76 Z: -3 -2 -1 2 57. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The area below z = 1.3. (b) The area below z =-1.3. (c) The area above z = 1.3. %3D (d) The area between z = -1.3 and z = 1.3. 58. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What is the probability that the average person has a time faster than Usain Bolt's record of 9.58 seconds? 59. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The z-score of the 45th percentile. 60. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What speed is the third quartile? Hint: The third quartile represents what percentile? (b) The z-score for the top 20%. 3.
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.
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