Question 2 The following probability distribution table shows the number of cars the top Sales Agents at Car Plus sells in a day and their corresponding probability. Number of cars, x 0 1 2 B 4 Probability, P(X = x) 0.10 0.20 0.30 a 0.05 a) Calculate the value of a b) On a typical day, how many cars should the top sales agent expect to sell? c) What is the variance of the distribution? [2] [3]
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- 25.100 Tossing a die. You are tossing a balanced die that has probability 1/6 of coming up 1 on each toss. Tosses are independent. We are interested in how long we must wait to get the first 1. (a) The probability of a 1 on the first toss is 1/6. What is the probability that the first toss is not a 1 and the second toss is a 1? (b) What is the probability that the first two tosses are not 1s and the third toss is a 1? This is the probability that the first 1 occurs on the third toss. 4 (c) Now you see the pattern. What is the probability that the first 1 occurs on the fourth toss? On the fifth toss?2
- 1. Imagine a person who wants to find a job within two months. Define X corresponding to the outcome, such that X = 1 if the person finds a job and X = 0 otherwise. (a) Explain why X can be viewed as a random variable. What is the support of X? (b) Suppose the probability of finding a job is 0.75. What is the probability distribution of X? Be specific.6 Company “X Star" supplies electronic devices. Probability of purchasing a defective device is 0.3. Mr. Chang has purchased two devices. (a) What is the probability that at least one device purchased by Mr. Chang is good? (b) What is the probability that at least one device purchased by Mr. Chang is defective?The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?
- a. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places)1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.4
- 7. The amount spent by a customer on a Summer Cruise has a normal distribution with a mean of $95.60 and a standard deviation of $5. a) Calculate the probability that a randomly selected customer spends less than $95. b) The probability that customers spend more than x dollars is 0.2810. Find the value of r.10. Calculate a joint probability given data: -Sample of 9000 firms. 6000 have CEO with Bachelor's degree, 2300 have CEO with Master's Degree, 700 have CEO with Ph. D. Find probability that a randomly selected CEO has a Bachelor's Degree or a Ph. D.Explanation sir and tees ams