Question 4) e) and f) please Tonks
2 answers:
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Answer:
a) X: number of years of education
b) Sample mean = 13.5, Sample standard deviation = 0.4
c) Sample mean = 13.5, Sample standard deviation = 0.2
d) Decrease the sample standard deviation
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 13.5 years
Standard deviation,σ = 2.8 years
a) random variable X
X: number of years of education
Central limit theorem:
If large random samples are drawn from population with mean and standard deviation
, then the distribution of sample mean will be normally distributed with mean
and standard deviation
b) mean and the standard for a random sample of size 49
c) mean and the standard for a random sample of size 196
d) Effect of increasing n
As the sample size increases, the standard error that is the sample standard deviation decreases. Thus, quadrupling sample size will half the standard deviation.
Answer:
The expected number of times is 4.
Step-by-step explanation:
Looking at the question, we see that this follows a geometric distribution because it is asking for the expected number of trials hat will bring about the FIRST SUCCESS. The probability of success is
Since it is a geometric distribution, we know that the expected value of a random variable X, E(X) that follows a geometric distribution is given as:
E(X) = 1/p where p is the probability of success.
Therefore, the expected number of times will be
E(X) = 1/(1/p) = 1/(1/4) = 4.
Hence, the expected number of times is 4.