* O 19 63% Ô 12:50 PM Chapter 7 - Course Pack (1) - Read-only Chapter 7- Course Pack The Central Limit Theorem 1. Suppose x has a distribution with a mean of 20 and a standard deviation of 3. Random samples of size n = 36 are drawn. a. Is the sampling distribution of x normal? How do you know? b. What is the mean and the standard deviation of the sampling distribution of x? c. Find the z score corresponding to x = 19. d. Find P (x < 19). e. Would if be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 19? Why? 2. A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green, and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 64 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes exceeding 4.75. 3. Suppose x has a distribution with u = 15 and o = 14 a. If a random sample of size n = 49 is drawn, what is the standard error (or standard deviation) of the sampling distribution x? b. Find P (15
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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