An English professor assigns letter grades on a test according to the following scheme. A: Top 7% of scores B: Scores below the
top 7% and above the bottom 59% C: Scores below the top 41% and above the bottom 18% D: Scores below the top 82% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 75.7 and a standard deviation of 8.8. Find the numerical limits for a C grade. Round your answers to the nearest whole number, if necessary.
1 answer:
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Answer:
(i) 0.15708
(ii) 0.432488
(iii) 3
Step-by-step explanation:
Given that, 99% of people who fracture or dislocate a bone see a doctor for that condition.
There is only two chance either the person having fracture or dislocation of bone will either see the doctor or not.
As per previous data, if one person got a fracture or dislocation of bone, the chance of seeing the doctor is 0.99. Assuming this chance is the same for every individual, so the total number of people having fractured or dislocated a bone can be considered as Bernoulli's population.
Let p be the probability of success represented by the chances of not seeing a doctor by any one individual having fractured or dislocated a bone.
So, p=1-0.99=0.01
According to Bernoulli's theorem, the probability of exactly r success among the total of n randomly selected from Bernoulli's population is
(i) The total number of persons randomly selected, n=400.
The probability that exactly 5 of them did not see a doctor
So, r=5 , p=0.01
Using equation (i),
=0.15708
(ii) The probability that fewer than four of them did not see a doctor
(iii) The expected number of people who would not see a doctor
=3