The amount of time, in minutes, that a person must wait for a bus is uniformly

distributed between 0 and 15 minutes, inclusive. What is the probability that a person

waits fewer than 12.5 minutes? What is the probability that will be between 0.5 standard

deviation from the mean,

2. Slater customers are charged for the amount of salad they take. Sampling suggests

that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.

Let x = salad plate filling weight, find the expected Value and the Variance of x. What is

the probability hat a customer will take between 12 and 15 ounces of salad?

3. The average number of donuts a nine-year old child eats per month is uniformly

distributed from 0.5 to 4 donuts, inclusive. Determine the probability that a randomly

selected nine-year old child eats an average of;

a) more than two donuts

b) more than two donuts given that his or her amount is more than 1.5 donuts.

4. Starting at 5 pm every half hour there is a flight from Nairobi to Mombasa. Suppose that

none of these plane tickets are completely sold out and they always have room.

A bottle contains 4 laxative and 5 aspirin tablets. 3 tablets are drawn at random from the

bottle. Find the probability that; a) exactly one, b) at most 1 c) at least 2 are laxative

tablet.

2. Want is the probability of getting at most 2 diamonds in the5 selected without

replacement from a well shuffled deck?

3. A massager has to deliver 10 out of 16 letters to computing department the rest to

statistics department. She mixed up the letters and delivered 10 letters at random to

computing department. What is the probability that, only 6 letters for computing

department actually got there?

4. In a class there are 20 students. 6 are compulsive smokers and they always keep

cigarette in their lockers. One day prefects checked at random on 10 lockers. What is the

probability that they find cigarette in at most 2 lockers?

5. A box holds 8 green, 4 white and 8 red beads. 6 beads are drawn at random without

replacement from the box. What is the probability that 3 red, 2 green and 1 white beads

are drawn?

4. The scores from a state standardized test have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical Rule to find the following. a) What percentage of students have scores between 70 and 130? b) What percentage of students have scores between 55 and 1157 c) Where would approximately 99.9% of the fall between? Measure of variability 5. Test scores for a statistics class had a mean of 79 with a standard deviation of 4.5. Test scores for a calculus class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 81 on the statistics test and a 71 on the calculus test. Which score is higher based on the standard deviation? 6. A student scores 56 on a geography test and 285 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 10. Which score is lower based on the standard deviation?1. A certain random variable X has the probability density function (PDF) given by _ x + 1, 1 S x S 0 mx)' {1x, 03x3 1 and fx (x) = 0 , otherwise. (a) Find and sketch the cumulative density function (CDF) of X . (b) What is the standard deviation (0) of this random variable? (c) Determine the probability that the X is within two standard deviations of its mean, i.e., P(|X| 0). Show all the work Moving to the neal quran prevent change in the am Question 1 A mannud production process is well modeled by a Poisson process with a rate of T products per 10 minutes, Find the probability that ] products are produced in a - minute interval. Use Gamma Distribution. OF 0917611 OF 0 809178 0 0. 9.190627 OF. 0.891 765 Moving to the next question prevents changes to this anover. question Vol 23 acerFind the Standard Deviation of a Discrete Random Variable From Its Probability Density Function Question The table below represents the probability density function for the random variable X. Find the standard deviation of X. . Round the final answer to two decimal places. X P(X = X) m 2/5 2/5 Help Copy to Clipboard Download CSV Provide your answer below