Question

Let X be a random variable representing the compressive strength of concrete cubes from a particular mix. X has a normal distribution with mean and standard deviation 60.14 and 5.02 N/mm2, respectively.

a. The probability that the compressive strength of a cube is between its mean value and c is
0.30. In other words P(μ £ X £ c) = 0.30, where μ is the mean value given above. What is
the value of c?
b. Assume that each cube behaves independently of other cubes and the probability that a
cube will pass a compressive strength test is 0.80. What is the probability that in a sample
of 3 cubes, exactly 1 of them will pass the test?
c. The construction company also performs another test on the cubes. They have found that
the probability that a cube will pass this test is p = 0.80. Assuming that each cube
performs independently of the others, what is the probability that in a sample of 500 the
number of cubes that pass the test is at least 406? Apply any approximation that is
appropriate

Answer 1

This problem has 3 parts.The first one uses normal distribution second one involves binomial and the third one uses a mix of binomial and normal.

Solution is explanatory in nature.

Prerequisites-

Normal , standard normal probabilities and binomial distribution.