Final answer:
The probability density function for a uniform distribution is given by f(x) = 1 / (b-a) for a ≤ x ≤ b. To find the probability that a student will take between 35 and 45 minutes, you need to find the area under the probability density function between 35 and 45 minutes. To find the probability that a student will take no more than 30 minutes.
Step-by-step explanation:
The probability density function (PDF) for a uniform distribution is given by:
f(x) = 1 / (b-a) for a ≤ x ≤ b
Where a is the lower bound and b is the upper bound.
(b) To compute the probability that a student will take between 35 and 45 minutes, you need to find the area under the probability density function between 35 and 45 minutes.
Since the PDF is constant, this can be computed by finding the percentage of the range between 35 and 45 over the total range from 30 to 55.
(c) To compute the probability that a student will take no more than 30 minutes, you need to find the area under the probability density function up to 30 minutes.
Since the PDF is constant, this can be computed by finding the percentage of the range from 30 to 55 over the total range from 30 to 55.
(d) The expected amount of time it takes a student to complete the examination can be found by taking the average of the lower and upper bounds of the distribution.
(e) The variance for the amount of time it takes a student to complete the examination can be calculated using the formula Var(X) = (b-a)^2 / 12.
Using the given lower and upper bounds, you can substitute them into the formula to find the variance.