In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 69. A survey of U.S. adults found that 32% have an online account with their healthcare provider. You randomly select 70 U.S. adults and ask them whether they have an online account with their healthcare provider. Find the probability that the number who have an online account with their healthcare provider is (a) at most 15, (b) exactly 25, and (c) greater than 30. Identify any unusual events. Explain. (Source: Pew Research Center)
In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 69. A survey of U.S. adults found that 32% have an online account with their healthcare provider. You randomly select 70 U.S. adults and ask them whether they have an online account with their healthcare provider. Find the probability that the number who have an online account with their healthcare provider is (a) at most 15, (b) exactly 25, and (c) greater than 30. Identify any unusual events. Explain. (Source: Pew Research Center)
Solution Summary: The author illustrates how the normal distribution can be used to approximate the binomial distribution.
In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.
69. A survey of U.S. adults found that 32% have an online account with their healthcare provider. You randomly select 70 U.S. adults and ask them whether they have an online account with their healthcare provider. Find the probability that the number who have an online account with their healthcare provider is (a) at most 15, (b) exactly 25, and (c) greater than 30. Identify any unusual events. Explain. (Source: Pew Research Center)
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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