Respuesta :
Answer:
a) P(Xs<947)=0.1844
b) The sampling distribution has to be evaluated with the t-students distribution, as the population standard deviation is not known.
Step-by-step explanation:
We have a sample of n=20 weather stations, with a sample average lifetime of 947 days and a sample standard deviation of s=136 days.
The population mean lifetime is 975 days.
We have to calculate the probability of having a sample with mean of 947 days or less, given that the population mean is 975 days.
As the population standard deviation is unknown, we will use the t-value and estimate the population standard deviation with the sample standard deviation.
The t-value for a X=947 is:
[tex]t=\dfrac{X-\mu}{s/\sqrt{n}}=\dfrac{947-975}{136/\sqrt{20}}=\dfrac{-28}{30.4105}=-0.9207[/tex]
The degrees of freedom are:
[tex]df=n-1=20-1=19[/tex]
We can now calculate the probability of having a sample with mean of 947 days or less:
[tex]P(X<947)=P(t_{19}<-0.9207)=0.18438[/tex]
