A coin is tossed 50 times, and the number of times heads comes up is counted.Which of the following statements about the distributions of counts and proportions is FALSE?The distribution of the count of getting heads can be approximated with a normal distribution.The distribution of the count of getting tails can be approximated with a normal distribution.The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution.The count of getting heads is a binomial distribution.
Question
A coin is tossed 50 times, and the number of times heads comes up is counted.Which of the following statements about the distributions of counts and proportions is FALSE?The distribution of the count of getting heads can be approximated with a normal distribution.The distribution of the count of getting tails can be approximated with a normal distribution.The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution.The count of getting heads is a binomial distribution.
Solution
The statement that is FALSE is: "The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution."
Here's why:
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"The distribution of the count of getting heads can be approximated with a normal distribution." This is true because the number of times you get heads in 50 tosses is a binomial distribution, and binomial distributions can be approximated by a normal distribution when the number of trials is large (like 50).
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"The distribution of the count of getting tails can be approximated with a normal distribution." This is also true for the same reason as above. The number of tails is just the flip side of the number of heads.
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"The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution." This is FALSE. The normal approximation is valid when the number of trials is large. A sample size of 20 is generally not considered large enough for the normal approximation to be valid.
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"The count of getting heads is a binomial distribution." This is true. Each toss of the coin is a Bernoulli trial (a trial with two possible outcomes), and the count of successes (heads) in a fixed number of Bernoulli trials follows a binomial distribution.
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