7.8 Topic 8: The Binomial Distribution 63. Suppose X follows a Binomial distribution. Is X continuous or discrete? Explain in your own words. 64. A particular test has a 72% pass rate. A teacher decides to grade tests until 15 people have passed before stopping for a break. Let X = the number of tests graded before taking a break. Determine if X is binomial by stating and checking all four requirements. If X is binomial, summarize the distribution of X in shorthand notation. 65. Suppose 22% of students at a certain university are out of state students. A professor takes a random sample of 50 students. Let X = the number of out of state students in the sample. Determine if X is binomial by stating and checking all four requirements. If X is binomial, summarize the distribution of X in shorthand notation. 66. Sickle-cell disease is a group of inherited blood disorders that can cause pain, anemia, swelling, infections, and stroke. It affects about 0.3% of all Americans. Let X = the number of children in a family of 4 that have sickle cell disease. Determine if X is binomial by stating and checking all four requirements. If X is binomial, summarize the distribution of X in shorthand notation. 67. About 10% of the general population is left handed. However, about 25% of baseball players are left handed. (a) Let X population. State n and p. Find the expected number of left handers and the standard the number of left handers in a random sample of 25 people from the general deviation. (b) Let X = the number of left handers in a random sample of 25 baseball players. State n and p. Find the expected number of left handers and the standard deviation. 68. Suppose 22% of students at a certain university are out of state students. A professor takes a random sample of 50 students. Let X the number of out of state students in the sample. (a) How many students are expected to be out of state? By how much does this vary? (b) What is the probability that 10 will be out of state? (c) What is the probability that 10 or fewer will be out of state? (d) What is the probability that fewer than 10 will be out of state? 69. About 10% of the general population is left handed. However, about 25% of baseball players are left handed. Suppose we take a random sample of 30 baseball players and let X = the number of left handed players in the sample. (a) What is the probability that at most 8 are left handed? (b) What is the probability that 8 are left handed? (c) What is the probability that more than 12 are left handed? (d) What is the probability that at least 12 are left handed?

Q: 24. Find d²4 zP 2. xp 4=3x² +34-8

A: Differentiate two times

Q: Evaluate

A: Explanation of the answer is as follows

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A:

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A:

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A:

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A:

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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.