The population of IQ scores forms a normal distribution with a mean of μ= 100 and a standard deviation of σ= 15. What is the probability of obtaining a sample mean greater than M = 95, a. for a random sample of n = 9 people? b. for a random sample of n = 25 people?
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The standard error is calculated as the standard deviation divided by the square root of the sample size (n). a. For a sample size of 9, the standard error is 15/√9 = 5. b. For a sample size of 25, the standard error is 15/√25 = 3. Show more…
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8. IQ scores have a mean of µ=100 in the general population, and have a standard deviation of σ=15. You take a random sample of n=9 people. What is the probability that your sample mean will be M=95 or less?
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Let $x$ denote the IQ of an individual selected at random from a certain population. The value of $x$ must be a whole number. Suppose that the distribution of $x$ can be approximated by a normal distribution with mean value 100 and standard deviation 15. Approximate the following probabilities. (Hint: See Example 6.32 ) a. $P(x=100)$ b. $P(x \leq 110)$ c. $P(x<110)$ (Hint: $x<110$ is the same as $x \leq 109$.) d. $P(75 \leq x \leq 125)$
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