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Suppose the random variable Z is distributed according to the standard normal distribution

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Suppose the random variable Z is distributed according to the standard normal distribution. Determine P(0.50 < Z < 2.56). Group of answer choices 0.2491 .5 0.6863 0.3033 Flag question: Question 2 Question 2 1 pts Suppose the random variable Z is distributed according to the standard normal distribution. Determine P( Z < -1.25 or Z > 1.25 ). Group of answer choices 0.6056 0.7888 0.2112 .3944 Flag question: Question 3 Question 3 1 pts Suppose X is a normally distributed random variable with mean ? μ = 10 and variance ? σ 2 = 4. Find P(7 < X < 12). Group of answer choices 0.7745 0.0919 0.2255 0.4649 Flag question: Question 4 Question 4 1 pts Determine the number c such that P(-c < Z < c) = .97, where Z is a standard normal random variable. Group of answer choices 2.17 1.96 1.285 3 Flag question: Question 5 Question 5 1 pts Studies show that gasoline use for compact cars sold in the united States is normally distributed, with a mean of 27.0 miles per gallon (mpg) and a standard deviation of 5.0 mpg. What percentage of compact cars get 32.0 mpg or more? Group of answer choices 42.07% 15.87 % 84.13% 34.13% Flag question: Question 6 Question 6 1 pts In certain population of the herring Pomolobus aestivalis, the length of the individual fish follow a normal distribution. The mean length of the fish is 54.0 mm, and the standard division is 4.5 mm. What percentage of the fish are between 58 and 60 mm long. Group of answer choices 40.82% 9.49% 5% 0% Flag question: Question 7 Question 7 1 pts Suppose X is distributed according to a normal distribution with mean 100 and variance 64. What is the median of the distribution of X? Group of answer choices 100 84 0 108 116 92 Flag question: Question 8 Question 8 1 pts Suppose X is distributed according to the normal distribution with mean 31 and standard deviation 4. Determine the 85th percentile of the distribution of X. In other words, find the number c such that P(X < c) = 0.85. Group of answer choices 31-1.035*4 31+1.96*4 31 + 1.035*4 31-1.96*4 Flag question: Question 9 Question 9 1 pts Researchers discovered that the curved carapace (shell) length of green sea turtles is approximately normally distributed with mean 55.7 centimeters and standard deviation 11.5 centimeters. What maximum L should be so that 95% of the turtles captured have shell length less than L. Group of answer choices 70.4775 36.7825 55.7 74.6175 Flag question: Question 10 Question 10 1 pts A random sample of 225 observations were selected from a population with a mean ? μ = 20 and variance ? σ 2 = 144. Find mean and standard deviation of the sampling distribution of the sample mean. Group of answer choices mean = 20, s.d. = 12 mean = 20, s.d. = 0.64 mean = 0.9, s.d. = 12 mean = 0.9, s.d. = 0.8 mean = 20, s.d. = 0.8 Flag question: Question 11 Question 11 1 pts According to American Automobile Association, the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65. Assume that the standard deviation of such cost is $0.25. Suppose that a random sample of n=100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. What is the approximate probability that the sample has a mean fuel cost between $3.60 and $3.70? Group of answer choices 0.1586 1 0.9544 0.9772 Flag question: Question 12 Question 12 1 pts A random sample of 100 observations, Denote by X1, X2, ..., X100, were selected from a population with a mean ? μ = 40 and variance ? σ 2 = 400. Determine P(38 < bar{X} < 43), where bar{X} = (X1 + X2 + ... + X100)/100. Group of answer choices 0.0198 0 1 0.0919 0.7745