Suppose you throw 10 darts at a Cartesian plane, with X and Y coordinate of the dart following a standard normal distribution, N(0, 1). Each dart throw independent of each other. (a) Find the probability that each dart is between 3 units and 5 units awa; from the origin of the Cartesian plane.

Consider a normal distribution curve where 70-th percentile is at 12 and the 45-th percentile is at 7. Use this information to find the mean, μ, and the standard deviation, o, of the distribution. a) με b) σ =

A population of values has a normal distribution with μ=139.8μ=139.8 and σ=54.4σ=54.4. You intend to draw a random sample of size n=87n=87.a.) Find the probability that a single randomly selected value is greater than 121.1.P(X > 121.1) = b.) Find the probability that a sample of size n=87n=87 is randomly selected with a mean greater than 121.1.P(M > 121.1) =  (Here M is the mean of the sample)Enter your answers as numbers accurate to 4 decimal places.

Consider a normal distribution curve where 55-th percentile is at 11 and the 20-th percentile is at 8. Use this information to find the mean, u , and the standard deviation, o , of the distribution. a ) μ - b) σ-

Assume two normal distributions where μ1 = 0.0001, σ1 = 0.01, μ2 = -.0002, σ2 = 0.015, and ρ = .45. Using zs = { .814, .259 }, generate z1 and z2.

Let the X-values represent the times, in minutes, of preparation for a Statistics test; let the Y-values represent the points earned on the test. Assume that the sample of paired (X, Y) data is a simple random sample of quantitative data and the data have a bivariate normal distribution. Also, the scatterplot shows that the points approximate a straight-line pattern. If the sample has 35 pairs of values with (Zx,Zy,) = 11.41, and if we use a significance level of 0.05, calculate r and determine whether if there is sufficient evidence to support a claim of a linear correlation between X and Y.

The time it takes me to ride my bike to school is uniformly distributed between 27 minutes and 36 minutes What is the probability that I can ride my bike to school in under 35 minutes? Give your answer accurate to two decimal places.