X is a random variable that follows a normal distribution with a mean of 35 and a standard deviation of 7. The values of a and b are such that Pr(a<x<b) =0.95 where this is the middle of 95% of values. A and b are best represented by..?
The answer is a=21.28 and b=48.72
You can use the inverse normal function on your CAS. For the first value you are finding the when the area to the left of a is 0.025 (bottom 2.5%), so you would enter
)
, which gives
.
For the second value you are finding when the area to the left of b is 0.975 (top 2.5%), so you enter
)
, which gives
.
Here's another one I'm stuck on.
A certain variety of apples has mass, Xg such that X~N(120,20)
Apples are classified as large if they have a mass larger than 145g
Find the probability of a 'large' apple having a mass less than 165g.
I'm guessing its a conditional one. I tried working it out but didn't get the right answer. The answer is 0.884
It is conditional probability, so that's right. We know that the apple is large, so the mass must be more than 145g. We are finding the probability it is less than 165g, given that we know it is more than 145g. The intersection of the apple having a mass more than 145g and less than 165g is 145g<mass<165g. Using the conditional probability formula, we have
=\frac{\mathrm{Pr}((X<165)\cap(X>145))}{\mathrm{Pr}(X>145)})
}{\mathrm{Pr}(X>145)})
}{\mathrm{normcdf}(145,\infty,120,20)} \right ))
They made a mistake in the definition of the normal distribution. They gave it in the form
)
when it should be
)
.
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