ANSWER ASAP! A random sample of n = 100 observations is selected from a populati

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ANSWER ASAP!

A random sample of n = 100 observations is selected from a population with meu = 30 and sigma = 21. Complete parts a through f. Click the icon to view the table of normal curve areas. Describe the shape of the sampling distribution of x bar. Approximately normal Skewed left Uniform distribution Skewed right Find P(x bar greater than or equal to 28). P(x bar greater than or equal to 28) = (Round to four decimal places as needed.) Find P(22.1 less than or equal to x bar less than or equal to 26.8). P(22.1 less than or equal to x bar less than or equal to 26.8) = (Round to four decimal places as needed.) Find P(x bar less than or equal to 28.2). P(x bar less than or equal to 28.2) = (Round to four decimal places as needed.) Find P(x bar greater than or equal to 27.0). P(x bar greater than or equal to 27.0) = (Round to four decimal places as needed.)

Explanation / Answer

B)

By central limit theorem,

OPTION A: Approximately normal [ANSWER]

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c)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    28      
u = mean =    30      
n = sample size =    100      
s = standard deviation =    21      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.95      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.95   ) =    0.8289 [ANSWER]

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d)

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    22.1      
x2 = upper bound =    26.8      
u = mean =    30      
n = sample size =    100      
s = standard deviation =    21      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u) * sqrt(n) / s =    -3.76      
z2 = upper z score = (x2 - u) * sqrt(n) / s =    -1.52      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.0001
P(z < z2) =    0.0643
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.0642 [ANSWER]

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e)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    28.2      
u = mean =    30      
n = sample size =    100      
s = standard deviation =    21      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.86      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.86   ) =    0.1949 [ANSWER]

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f)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    27      
u = mean =    30      
n = sample size =    100      
s = standard deviation =    21      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.43      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.43   ) =    0.9236 [ANSWER]

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