4. Jane decided to sell her house. A random variable X models the number of passengers in cars arriving at the auction for Jane's house. X takes values of 0 or 1 or 2 or 3. The probabilities it takes the values 1, 2, or 3 are 0.3, 0.2, and 0.1 respectively. (a) Find the mean value of X. (b) Find the standard deviation of X.
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- A collection of numbers is Normal with a Mean of 20 and a Standard Deviation of 5; that is N(20,5). Boris’s score is 23.7 and Bela’s score is 26.2. What is the probability that a score is greater than Boris and less than Bela? Your final answer should be correct to 3 places after the decimal point. ________Verify whether the given table represents a probability distribution. In those cases where a probability distribution is described, find the mean and standard deviation. NOTE: The Rounding Rule for the mean and standard deviation: They should be rounded to one more decimal place than occurs in the raw data. For a group of four students, the number y who takes the Calculus II class next semester is given by this table. y P(y) 0 0.5131 1 0.3139 2 0.0624 3 0.1102 4 0.2002 Probability distribution with μ=0.4 and σ=0.4 Probability distribution with μ=0.6 and σ=0.1 Probability distribution with μ=0.6 and σ=0.3 Probability distribution with μ=0.7 and σ=0.4Empirical research on stock market data for two consecutive trading days indicates that 60% of the stocks that went up on the first day also went up on the second day. Yesterday, 600 stocks went up. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p gives the proportion of the 600 stocks that went up yesterday that will go up today. (b) Find the standard deviation of p. (c) Compute an approximation for P(p <0.58), which is the probability that fewer than 58% of the stocks that went up yesterday will go up again today. Round your answer to four decimal places.
- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 240 feet and a standard deviation of 48 feet. Let X = distance in feet for a fly ball. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 186 feet? (Round your answer to four decimal places.) ch6#4The average amount of snow per season in Trafford is 45 inches. The standard deviation is 5 inches. Use a graphing calculator to find the probability that next year Trafford will receive the given amount of snowfall. Assume the random variable is normally distributed. Round your answers to 3 decimal places. Part: 0/2 Part 1 of 2 (a) Find the probability Trafford will receive at most 54 inches of snow. The probability that Trafford will receive at most 54 inches of snow is XThe percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. Part (a) Give the distribution of X. X-N 36 10 Part (b) Find the probability that the percent of fat calories a person consumes is more than 40. (Round your answer to four decimal places.) X
- The probability distribution for the number of students in Statistics classes offered at a small college is given, but one value is missing. Fill in the missing value, then answer the questions that follow. X P(X) 22 0.18 23 0.22 24 0.25 25 26 0.2 Find the mean number of students in a Statistics class at the college: Find the standard deviation of the number of students in a Statistics class at the college:Q29show complete solution, thank you.
- Fill in the blanks: The random variable Y has the probability distribution given the following table. у: 2 3 4 5 6 7 P (Y = y): 0.15 0.1 a 0.25 0.11 0.2 Determine the standard deviation of Y.10 An instructor of statistics claims that students in his section will score smaller than the students in a colleague’s section. The mean statistics score for 33 students in his section is 25.5 and the standard deviation is 4.1. The mean statistics score for 31 of the colleague’s students is 26.7 and the standard deviation is 4.5. At a = 0.01. Can the instructor’s claim be supported? According to this information the null and alternative hypotheses are: Select one: a. H0: μ1 ≤ μ2Ha: μ1 > μ2 b. H0: μ1 ≥ μ2 Ha: μ1 < μ2 c. H0: μ1 < μ2 Ha: μ1 > μ2 d. H0: μ1 > μ2 Ha: μ1 ≤ μ2