A report stated that the day-care cost per week in Boston is $109. If this figur

Question

A report stated that the day-care cost per week in Boston is $109. If this figure is taken as the mean cost per week of day-care in Boston and if the standard deviation were known to be $20, find the probability that a sample of 50 day-care centers would show a mean cost of $100 or less per week. Show your work. A report stated that the day-care cost per week in Boston is $109. If this figure is taken as the mean cost per week of day-care in Boston and if the standard deviation were known to be $20, find the probability that a sample of 50 day-care centers would show a mean cost of $100 or less per week. Show your work. A report stated that the day-care cost per week in Boston is $109. If this figure is taken as the mean cost per week of day-care in Boston and if the standard deviation were known to be $20, find the probability that a sample of 50 day-care centers would show a mean cost of $100 or less per week. Show your work. A report stated that the day-care cost per week in Boston is $109. If this figure is taken as the mean cost per week of day-care in Boston and if the standard deviation were known to be $20, find the probability that a sample of 50 day-care centers would show a mean cost of $100 or less per week. Show your work.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    100      
u = mean =    109      
n = sample size =    50      
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -3.181980515      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -3.181980515   ) =    0.000731358 [ANSWER]

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