Please show your work stepbystep Work on problem number 15 a

Please show your work step-by-step.

Work on problem number 15 (a-c) on page 7-70

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    55      
u = mean =    52      
n = sample size =    10      
s = standard deviation =    4.74341649      
          
Thus,          
          
z =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 [ANSWER, PART A]

**********************************

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    50      
x2 = upper bound =    60      
u = mean =    52      
n = sample size =    10      
s = standard deviation =    4.74341649      
          
Thus, the two z scores are          
          
z1 = lower z score =    -1.333333333      
z2 = upper z score =    5.333333333      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.09121122      
P(z < z2) =    0.999999952      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.908788732   [ANSWER, PART B]  

*****************************************

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    55      
u = mean =    52      
n = sample size =    10      
s = standard deviation =    4.74341649      
          
Thus,          
          
z =    2      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   2   ) =    0.977249868 [ANSWER, PART C]