Probability and Statistics with R - Statistics Assignment Help

Assignment Task:

Task:

1. If a random variable has the normal distribution with μ= 77.0 and σ = 3.4, find the probability that random variable is:
a. less than 72.6
b. greater than 88.5
c. between 81 and 84
d. between 56 and 92

2. In a car race, the finishing times are normally distributed with mean 145 minutes and standard deviation of 12 minutes.
a. Find percentage of car racers whose finish time is between 130 and 160 minutes.
b. Find percentage of car racers whose finish time is less than 130 minutes.

3. A test-taker has recently taken an aptitude test with 15 questions. All the questions are True/ False type in nature.
a. What is the probability that the student got first five questions correct?
b. What is the probability that the student got five questions correct?

4. 68% of the marks in exam are between 35 and 42. Assuming data is normally distributed, what are the mean and standard deviation?

5. A professor asked students to take two exams. 30% of the class cleared both exams and 55% of the class cleared the first exam. What percentage of class who cleared first exam also cleared the second exam?

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