There is u very popular lottery in which a ticket is called a scratcher. In this lottery, 43% of the scratchers are winning ones. Suppose that we will take a random sample of 10 scratchers. Let p represent the proportion of winning scratchers from the sample. Consider the sampling distribution of the sample proportion p. Complete the following. Carry your intermediate computations to four or more decimal places. Write pur answers with two decimal places, rounding if needed (a) Find LA (the mean of the sampling distribution of the sample proportion). HA =| (b) Find on (the standard deviation of the sampling distribution of the sample proportion).
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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### Sampling Distributions of a Sample Proportion
There is a very popular lottery in which a ticket is called a scratcher. In this lottery, 43% of the scratchers are winning ones. Suppose that we will take a random sample of 10 scratchers. Let \( \hat{p} \) represent the proportion of winning scratchers from the sample. Consider the sampling distribution of the sample proportion \( \hat{p} \).
Complete the following steps. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed.
#### (a) Find \( \mu_{\hat{p}} \) (the mean of the sampling distribution of the sample proportion).
\[ \mu_{\hat{p}} = \boxed{} \]
#### (b) Find \( \sigma_{\hat{p}} \) (the standard deviation of the sampling distribution of the sample proportion).
\[ \sigma_{\hat{p}} = \boxed{} \]
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This educational content is designed to help students understand and calculate the mean and standard deviation of the sampling distribution of sample proportions in the context of a lottery game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e9fa55-7beb-4d98-aad2-e62c3133051d%2Ff6dc5482-4122-4a94-9c59-0ec8acb672ca%2Fa9lvaw5_processed.jpeg&w=3840&q=75)
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