A random sample of sizen= 150 is taken from an infinite population with mean=5 and variance 10. a. Use the result of the Central Limit Theorem to determine the probability that X will fall between 4.5 and 5.2. b. Would your answer to part "a" change if the population variance is unknown and we estimate the population variance using the sample variance = 10? Explain your answer and be sure to discuss any assumptions needed.
A random sample of sizen= 150 is taken from an infinite population with mean=5 and variance 10. a. Use the result of the Central Limit Theorem to determine the probability that X will fall between 4.5 and 5.2. b. Would your answer to part "a" change if the population variance is unknown and we estimate the population variance using the sample variance = 10? Explain your answer and be sure to discuss any assumptions needed.
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
Transcribed Image Text:A random sample of size n = 150 is taken from an infinite
population with mean=5 and variance = 10.
a. Use the result of the Central Limit Theorem to determine the
probability that X will fall between 4.5 and 5.2.
b. Would your answer to part “a" change if the population
variance is unknown and we estimate the population variance
using the sample variance = 10? Explain your answer and be sure
to discuss any assumptions needed.
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Step 1
Given
Sample size = 150
Mean = 5
Variance = 10
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