Question 1200150
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Part (b)


On your TI84 calculator, press the button labeled "2nd" in the upper left corner.
Then press the VARS key to bring up the stats distribution menu.


The function we're after is <font color=blue>normalcdf</font> which finds the area under the normal distribution curve.


The template is <font color=blue>normalcdf(L, U, mu, sigma)</font>
L = lower boundary
U = upper boundary
mu = mean
sigma = standard deviation


In the case of part (b), we have
L = 17
U = 9999, or any other very large value to represent positive infinity
mu = 15
sigma = 6


This means you would type in <font color=blue>normalcdf(17,9999,15,6)</font>


Your calculator should produce the approximate result of 0.3694414037 which rounds to 0.3694 when rounding to four decimal places.


Answer to part (b): <font color=red size=4>0.3694</font>


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Part (d)


We're looking for a value of k such that
P(X < k) = 0.80
we want to know the cut-off point between the lower 80% and the upper 20%


The function we want is called <font color=blue>invNorm</font> 
This can be found in the same menu as normalcdf. It's in the 3rd slot.


The template for this function is
<font color=blue>invNorm(p, mu, sigma)</font>
where,
p = area under the normal curve between 0 and 1
mu = mean
sigma = standard deviation


In this case,
p = 0.80
mu = 15
sigma = 6


So you should type in <font color=blue>invNorm(0.80, 15, 6)</font>
The calculator will produce a result of roughly 20.0497274
That rounds to 20 when rounding to the nearest whole number.


So we can say that
P(X < 20) = 0.80
approximately.


About 80% of the trials finish within 20 days (i.e. 20 days or fewer).


Answer to part (d) is <font color=red size=4>20</font>
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