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Answer:
<em>a) P(x<1200)=74.14%</em>
<em>b) P(1100<X<1250)=57.54%</em>
Step-by-step explanation:
<u>Normal Distribution</u>
The normal distribution, also known as the bell curve, is a distribution that occurs naturally in many situations of life. We use the model to understand the behavior of some real-life variables. Where
is the mean value and
is the standard deviation.
In our case, we have
And are required to find the percentage of steers whose weigh lie within a given range. We must use some sort of table or digital means to compute the values because the normal distribution cannot be calculated directly by a formula. We use the NORMDIST (or NORM.DIST) formula for Excel which gives us the left tail of the area behind the bell curve, i.e. the cumulative percentage for a give value of X. The formula has the form
NORM.DIST(x,mean,standard_dev,cumulative)
a) X<1200
The formula is used with the following parameters
NORM.DIST(1200,1143,88,true)
and we get
b) We need to compute P(1100<X<1250). To do this, we calculate both left tails and the subtract them
NORM.DIST(1100,1143,88,true)=0.3125
NORM.DIST(1250,1143,88,true)=0.8880