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Determine whether each of the...

Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x1234 P(x)1/125/121/31/12 (B) x368 P(x) 2/10.51/5 (C) x20354050 P(x)0.4-0.20.50.3 2.Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5 i. Find the probability that x = 3 using the binomial tables ii. Use the normal approximation to find the probability that x = 3. Show all work. 3. The diameters of oranges in a certain orchard are normally distributed with a mean of 6.85 inches and a standard deviation of 0.80 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.3 inches? (B) What percentage of the oranges in this orchard are larger than 6.75 inches? (C) A random sample of 100 oranges is gathered and the mean diameter obtained was 6.75. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 6.75 inches? (D) Why is the z-score used in answering (A), (B), and (C)? (E) Why is the formula for z used in (C) different from that used in (A) and (B)? 4. Assume that the population of heights of female college students is approximately normally distributed with mean m of 69 inches and standard deviation s of 6.75 inches. A random sample of 16 heights is obtained. Show all work. (A) Find the proportion of female college students whose height is greater than 66 inches. (B) Find the mean and standard error of the distribution (C) Find P(-/x >66) 5.Answer the following questions regarding the normal, standard normal and binomial distributions. (A) Why can the normal distribution be used as an approximation to the binomial distribution? (B) What conditions must be met in order to use the normal distribution to approximate the binomial distribution? (C) Why is the correction for continuity necessary when the normal distribution is used to approximate a binomial distribution? 6. . Four jelly beans are selected, one at a time from a bowl containing 6 black, 6 red and 6 green jelly beans. Let x represent the number of black jelly beans selected in 4 draws from the bowl. (A) If this experiment is completed without replacing the jelly beans, explain why x is not a binomial random variable. (B) If this experiment is completed with replacement of the jelly beans, explain why x is a binomial random variable. 1. Find the following probabilities: (A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3 and P(A or B) = 0.70, find P(B). (B) Events A and B are defined on a common sample space. If P(A) = 0.40, P(B) = 0.50, and P(A or B) = 0.50, find P(A and B) 2. A small bag of Skittles candies has the following assortment: red (12), blue (5), orange (15), brown (0), green (16), and yellow (7). Construct the probability distribution for x. 3. Find the mean and standard deviation of the following probability distribution: x123 P(x)0.40.250.35 4. Classify the following as discrete or continuous random variables. (A) The time it takes to run a marathon (B) The number of fractions between 1 and 2 (C) A pair of dice is rolled, and the sum to appear on the dice is recorded (D) The length of a broad jump 5. In testing a new drug, researchers found that 10% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probability that: (A) exactly three will have this mild side effect (B) at least three will have this mild side effect. 6. X has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities: (A) P(x < 65.0) (B) P(66.0 < x < 72.0) (C) P(x>73.0) 7. Find the value of z such that 49.5% of the distribution lies between it and the mean. 8. Assume that the average annual salary for a worker in the United States is $36,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,000. Find the following: (A) What percentage of Americans earn below $26,000? (B) What percentage of Americans earn above $39,000?

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Level/Year: 2nd year college

Subject: stats

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I tried using brainmass but I'm not sure about them.

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Level/Year: 2nd year college

Subject: stats

Already Tried:

I tried using brainmass but I'm not sure about them.

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