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Answer:a) Quantitative ,ratiob) Quantitative, intervalc) Categorical, ordinal2. Fill in the values in the table below to give a legitimate probability distribution for the discrete random variable ?, whose possible values are ?,?,?,?, and .Value x of X P(X=x) -2 0.23 0 0.22 2 0.15 3 ? 6 ?Answer: Put 0.3 and 0.13. Let be a random variable with the following probability distribution: Value of 400.25500.15600.20700.05800.10900.25Find the expectation and variance of .Answer:E(x)=63.5V(X)=372.754. Let be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.P(Z> 1.62) = 0.053P( Z lesser or equal to – 0.62)=0.268P(1.15< Z< 1.85)=0.0935. Let be a standard normal random variable. Use the calculator provided to determine the value of such that . Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.Answer: -0.876. Suppose that the heights of adult women in the United States are normally distributed with a mean of inches and a standard deviation of inches. Jennifer is taller than of the population of U.S. women. How tall (in inches) is Jennifer? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.Answer: 67.17. An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of and a standard deviation of . The individuals who exceed on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders? Round your answer to at least four decimal places.Answer: 0.1492 8. Use the calculator provided to solve the following problems.Consider a t distribution with degrees of freedom. Compute . Round your answer to at least three decimal places.Consider a t distribution with degrees of freedom. Find the value of such that . Round your answer to at least three decimal places. P (-1.14 < t < 1.14) = 0.736 C= 1.7069. Let be a standard normal random variable. Use the calculator provided to determine the value of such that . Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.Answer: -0.6310. According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard deviation of inches. What is the probability that the mean daily precipitation will be inches or more for a random sample of November days (taken over many years)? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.Answer: 0.376\s11. \s12. X3.0873.1313.2413.2413.2703.3533.4003.4003.4083.4113.4353.4373.4373.4393.477 ................
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