Suppose that the average number of Facebook friends users have is normally distributed with a mean of 111 and a standard deviation of about 50. Assume eleven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) For the group of 11, find the probability that the average number of friends is less than 110.
Suppose that the average number of Facebook friends users have is
- What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
- For the group of 11, find the
probability that the average number of friends is less than 110.
1.
Central Limit Theorem for mean:
If a random sample of size n is taken from a population having mean and standard deviation then, as the sample size increases, the sample mean approaches the normal distribution with mean and standard deviation σ/ sqrt(n).
Sampling distribution of the sample mean:
The mean of the sampling distribution is given as μx-bar = 111.
The population standard deviation is, σ =50. The sample size is, n = 11.
The standard deviation using central limit theorem is σ/√n= 50/√11 = 15.08.
Thus, the sampling distribution of the sample mean for sample of size 11 follows normal distribution with mean μx-bar = 111 and standard deviation 15.08.
x-bar ~N(111,15.08).
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