Lee Philips,estimates that Biolab Inc. should earn $2 per share in 20X1,with a standard deviation of $1.If Biolab’s
earnings outcomes are normally distributed,the probability that Biolab earns $3 or more in 20X1 is closest to
A. 16%
B.32 %
C 34%.
Ans 16%
I’m assuming the sample size isn’t an issue, and that you can use the z table.
The question is asking for probability in the right tail.
Standardize the numbers to get a normalized value: ($3 - $2)/$1 = $1.
Go to the z table and look for 1.0. The value is 0.8413. However, when you read a z table, the value is good for probability in the left tail. In this question, they’re asking for the probability in the right tail.
So you subtract 0.8413 from 1.0 to get ~16%.
Once you understand the symmetric nature of the bell curve, you can take a shortcut and just look up the probability for -1.0 instead of +1.0 in the z table.
Hope this helps.
Oh dear, it more than helps.thank you so much.wow !never taught of the question like that.
Alternately, you could use the fact that in a normal distribution, approximately 68% of the distribution falls within 1 std deviation of the mean. So, 32% falls outside that range. Since the distribution is symmetric, 16% falls above +1 std deviation from the mean and 16% falls below -1 std deviation.
Alternately, you could use the fact that in a normal distribution, approximately 68% of the distribution falls within 1 std deviation of the mean. So, 32% falls outside that range. Since the distribution is symmetric, 16% falls above +1 std deviation from the mean and 16% falls below -1 std deviation.
This logic may work for this question, but you really need to know how to interpolate the exact value using the z-table. I’d definitely fvck around with exam takers by sliding in an option like 15.9%.
Also, be ready for questions that force you to do reverse lookups. That is, they will supply you with the probability and ask you for the normalized value. If I wanted to make the question very hard, I’d ask you to go a step further and have you use the normalized value to find the standard deviation or the mean.
Once you understand the logic, these are easy points on the exam!
Drawing a picture is also a good idea.
Agree. Drawing a picture is the best way to solve these kinds of questions.
draw out the normal distribution curve…mark out the >$3 part…look at the z table…find the right tail area…
hope i got this right