The reading speed of second grade students is approximately

The reading speed of second grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm .

a. (1 pt.) What is the probability a randomly selected student will read more than 95 words per minute?

b. (1 pt.) If a random sample of 24 second grade students was taken, what would be the mean, standard deviation and shape of the distribution of sample means?

c. (1 pt.) What is the probability that a random sample of 24 second grade students results in a mean reading rate more than 95 words per minute?

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    95      
u = mean =    90      
          
s = standard deviation =    10      
          
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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b)

It would be bell shaped, according to the central limit theorem.

It will have the same mean, ux = 90 wpm.

The standard deviation of it is sigma/sqrt(n) = 10/sqrt(24) = 2.041241452 [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 =    95      
u = mean =    90      
n = sample size =    24      
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.449489743      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.449489743   ) =    0.007152939 [ANSWER]