A random sample is drawn from a normally distributed population with mean p = 11 and standard deviation o = 1.7. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n= 20 and n= 35 normally distributed? O Yes, both the sample means will have a normal distribution. O No, both the sample means will not have a normal distribution. O No, only the sample mean with n= 20 will have a normal distribution. O No, only the sample mean with n= 35 will have a normal distribution. b. Calculate the probabilities that the sample mean is less than 11.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability 20 35
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A random sample is drawn from a
a. Are the sampling distribution of the sample mean with n=20 and n=35 normally distributed?
Multiple choice:
1 yes both the smaple means will have a normal distribution.
2. No both the sample means will not have a normal distribution.
3. No only the sample mean with n=20 will have a normal distribution.
4. No only the sample mean with n=35 will have a normal distribution.
b. Calculate the probabilities that the sample mean is less than 11.6 for both
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![A random sample is drawn from a normally distributed population with mean p = 11 and standard deviation o = 1.7. [You may find it
useful to reference the z table.]
a. Are the sampling distribution of the sample mean with n= 20 and n= 35 normally distributed?
O Yes, both the sample means will have a normal distribution.
O No, both the sample means will not have a normal distribution.
O No, only the sample mean with n= 20 will have a normal distribution.
O No, only the sample mean with n= 35 will have a normal distribution.
b. Calculate the probabilities that the sample mean is less than 11.6 for both sample sizes. (Round intermediate calculations to at least
4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)
Probability
20
35](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecea214b-1718-4bd7-bd57-2ed6bf391891%2F3aa11b6d-08e4-4764-a9b3-a86fe9f0cea1%2Frv6uimf.jpeg&w=3840&q=75)
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