A normal distribution of scores in populationhas a mean of 1

A normal distribution of scores in populationhas a mean of 100 with a standard deviatiion of 20.

What is the probability of randomly selecting a score greater than X= 110 rom this population?

*If a sample of n=25 scroes is randomly selected from this population, what is the probability thaqt the sample mean will be greater than M= 110?

*I only need help with this question.

Solution

1. What is the probability of randomly selecting a score greater than X= 110 rom this population?

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    110      
u = mean =    100      
          
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) / s =    0.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.5   ) =    0.308537539 [ANSWER]

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2. If a sample of n=25 scroes is randomly selected from this population, what is the probability thaqt the sample mean will be greater than M= 110?

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    110      
u = mean =    100      
n = sample size =    25      
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.5   ) =    0.006209665 [answer]

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