For a normal population with a mean equal to 80 and standard deviation equal to

Question

For a normal population with a mean equal to 80 and standard deviation equal to 16
Determine the probability of observing a sample mean of 85 or less from a sample of size 16.
Construct a 95% confidence interval for the sample mean from a sample size of 25 For a normal population with a mean equal to 80 and standard deviation equal to 16
Determine the probability of observing a sample mean of 85 or less from a sample of size 16.
Construct a 95% confidence interval for the sample mean from a sample size of 25
Determine the probability of observing a sample mean of 85 or less from a sample of size 16.
Construct a 95% confidence interval for the sample mean from a sample size of 25

Explanation / Answer

mean is 80 and standard deviation s is 16

standard error SE=s/sqrt(n)=16/sqrt(16)=4

z is given as (x-mean)/s

P(xbar<85)=P(z<(85-80)/4)=P(z<1.25) , from normal table we get 0.8944

Standard error SE for s/sqrt(n)=16/sqrt(25)=3.2

z for 95% confidence is 1.96

lower bound is mean-z*SE= 80-1.96*3.2=73.728

upper bound is mean+z*SE= 80+1.96*3.2=86.272

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