Let X be normally distributed with mean μ = 4.3 and standard deviation σ = 2 Find x such that P(X > x) = 0.0869
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- Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)Suppose that the heart beat per minute (bpm) of adult males has a normal distribution with a mean of mu equals 68μ=68 bpm and a standard deviation of sigma equals 11.3σ=11.3 bpm. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater)less than or equals≤0.01 and a value is significantly low if P(x or less)less than or equals≤0.01. Find the pulse rates for males that separate significant pulse rates from those that are not significant. Using these criteria, is a male pulse rate of 90 beats per minute significantly high?The random variable X has an exponential distribution: X ~ Exponential(0.2). Find the following: (a) P(2 < X < 10) (b) P(X > 6) (c) Find the 70th percentile for X
- A population of values has a normal distribution with μ=216.7μ=216.7 and σ=12.4σ=12.4. You intend to draw a random sample of size n=186n=186.What is the mean of the distribution of sample means?μ¯x=μx¯= What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)σ¯x=σx¯=Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 4.3 and standard deviation ? = 0.5. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) < z(b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)z < (c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) < z < (d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.)x < (e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.) < x(f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.) < x <Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value x, that represents the 80th percentile of the distribution %3D Enter your answer accurate to TWO decimal places.
- IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 99, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 99. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value -1 -1.5 0 +). Click and drag the arrows to adjust the values. 1 2 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement. Edit Insert Formats B I U x₂ x² A => EM e & N 18 (f) The middle 50% of IQs fall between what two values? (g) Sketch the graph and write the probability statement. Edit Insert Formats BIUX₂ X² A E = = E EC P R N • Σ+ Σ Α Σ+ Σ ΑLet X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value xo that represents the 80th percentile of the distribution. Answer should be accurate to two decimal places.Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation A. Compute a 98% CI for true average porosity of another seam based on n specimens with a sample average porosity of B. n=21 B=5.1 A=0.8 What is the upper bound? Two decimal places
- If X is normally distributed and P(X<20)=0.5 and P(X>26)=0.0228, find the mean and standard deviation of X. Give a detailed solutionA population of values has a normal distribution with u = 10.3 and o = random sample of size n = 199. 89.3. You intend to draw a What is the mean of the distribution of sample means? Hx = E(X) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) SD(X)
