Suppose that the number of times a high school student says

Suppose that the number of times a high school student says “like” in a sentence is approximately normally distributed with a mean of 4 and a standard deviation of .5.

a)what percentage of high schoolers say “like” in a sentence more than 5 times?

b.For high schoolers, what is the 86^th percentile for the number of times that “like” is said in a sentence

Solution

a)
We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    5      
u = mean =    4      
          
s = standard deviation =    0.5      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 = 2.2750132% [ANSWER]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.86      
          
Then, using table or technology,          
          
z =    1.080319341      
          
As x = u + z * s,          
          
where          
          
u = mean =    4      
z = the critical z score =    1.080319341      
s = standard deviation =    0.5      
          
Then          
          
x = critical value =    4.54015967   [ANSWER]