What is x in your problem? This information should be given to you, but I'll assume that x is the mean from your sample of size 100.
There are two standard deviations in play here: (1) the standard deviation of the population from which you drew your sample [=200], and (2) the standard deviation of the sampling distribution for the mean [according to the central limit theorem, this is equal to (pop std dev)/sqrt(N) = 200/sqrt(100) = 20, where N is your sample size].
So (a) is asking what is the probability that the mean from a sample of size 100 will be greater than 480. According to the CLT, the sampling distribution for the sample means is normal with a mean of 500 and standard deviation of 20. So you need to calculate a z-score = (480 - mu)/sigma = (480-500)/20 = -1. You need to look this value up on a table to find the area under the normal curve above -1.
There are two standard deviations in play here: (1) the standard deviation of the population from which you drew your sample [=200], and (2) the standard deviation of the sampling distribution for the mean [according to the central limit theorem, this is equal to (pop std dev)/sqrt(N) = 200/sqrt(100) = 20, where N is your sample size].
So (a) is asking what is the probability that the mean from a sample of size 100 will be greater than 480. According to the CLT, the sampling distribution for the sample means is normal with a mean of 500 and standard deviation of 20. So you need to calculate a z-score = (480 - mu)/sigma = (480-500)/20 = -1. You need to look this value up on a table to find the area under the normal curve above -1.
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