Statistics and Probability Answers

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 19 minutes and a standard deviation of 2 minutes.

​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​half-price. What percent of customers receive the service for​ half-price?

​(b) If the automotive center does not want to give the discount to more than 2​% of its​ customers, how long should it make the guaranteed time​ limit?

Suppose x is a normally distributed random variable with μ=46 and σ=3. Find a value x0 of the random variable x that satisfies the following equations or statements.

a.​ 10% of the values of x are less than x0.

b.​ 80% of the values of x are less than x0.

c.​ 1% of the values of x are greater than x0.

Find the value of zα.

α=0.26

(a) Gideon rolls two (2) six-sided dice once. What is the probability that the sum of the

outcomes of both dice are odd or divisible by 5?

(b) Two (2) dice are rolled. What is the conditional probability that at least one lands on 6 given that the dice land on two different numbers?

A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. One percent of the population actually has the disease. Calculate the probability that a person has the disease given that the test indicates the presence of the disease.

(a) Two numbers are chosen at random from among the numbers 1 to 10 without

replacement. Find the probability that the second number chosen is 5.

(b) A box contains 8 yellow, 5 green and 7 black balls identical to each other except for colour. 3 balls are drawn at random one after the other without replacement. Find the probability that:

(i) there will be one ball of each colour.

(ii)exactly one ball will be black

(iii) at least one ball will be black

(iv) the second ball will be black

(v) the second ball will be black given that the first is black.

Let X1, X2, X3, X4 be random variables that are all independent of each other and have the same distribution, namely, P(X1 = 1) = 0.2, P(X1 = 0) = 0.8, and identically so for X2, X3, X4. Calculate the probability that P(X1 + X2 + X3 + X4 <= 3)?

Given that a light bulb will have a lifespan of three months averagely with ........ a standard deviation of one month. Let five of these following light bulbs indicate the lifespan (in months) ......... ......... 4.2, 2.4, 3.5, 1.9, 3.0 ......... Can we still claim that the light bulbs have a standard deviation of 1 month? Assuming that the light bulb lifetime follows a normal distribution. 

Suppose that a set of data 3, 3, 4, 5, 6 and 7 indicating the number of students graduated from their doctorate degree by a random sample of 6 universities in Malaysia. Find the standard deviation of the aforementioned dataset.