Let X be the number of students who show up for a professor's office hour on a particular day. Suppose that the pmf of X is p(0) = 0.10, p(1) = 0.25, p(2) = 0.20, p(3) = 0.30, and p(4) = 0.15. (a) Draw the corresponding probability histogram. 0.30- 0.30 0.30 0.30- 025 0.25 025 025 0.20 020 020 E0.15 E 0.15 E015 E 0.15 0.10 0.10 0.10 0.10 0.05 aas 0.00 a.00 a.00 a00 1 2 3 4. 1 3 4. 3 (b) What is the probability that at least two students show up? More than two students show up? (c) What is the probability that between one and three students, indlusive, show up?

Let Y be an exponential random variable with (unknown) mean 0.

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

Samuel F.B. Morse (1791 – 1872), the creator of Morse Code, claimed that 12% of all letters used in the English language were “e”s.  Suppose random samples of 196 letters are selected from a book What is the probability that a random sample of 196 letters will contain at least 10% "e"s? Type your calculated z-score here. Express its value to the nearest hundredth (two decimal places).  Type your probability here. Express its value to four decimal places. Do not round.

The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr

Find the probability ​P(Ec​) if ​P(E)=0.17.

Question 4 According to the WHO, the birth weight for male babies born full-term is normally distributed with a mean 90.1 oz and a standard deviation of 17.3 oz. Let X be the birth weight of a randomly selected male baby born full-term. 1. Describe the probability distribution of X and state its parameters and σ: X Select an answer Select an answer XTBZEN a. less than 128.5 oz. b. between 61.9 and 82.1 oz. c. more than 131.7 oz. X² (μ = 2. Find the probability that the birth weight of a randomly selected male baby born full-term is 3. Find the 65-th percentile for the birth weight. 0 = (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) oz (Round the answer to 1 decimal place)

The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr