1 For a random variable with 11815 and 2807 the probabilit

1. For a random variable with = 118.15 and = 28.07, the probability that a simple random sample of 35 items will produce a mean that is greater than 120.00 is equal to the probabilty that z is greater than

. 2.For a random variable with = 119.05 and = 27.85, the probability that a simple random sample of 37 items will produce a mean that is less than 119.00 is equal to the probabilty that z is less than.

Solution

1.

We get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    120      
u = mean =    118.15      
n = sample size =    35      
s = standard deviation =    28.07      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.38990907   [ANSWER]

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2.

We get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    119      
u = mean =    119.05      
n = sample size =    37      
s = standard deviation =    27.85      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.010920579   [ANSWER]