T-curve probability density curve F-curve Chi-square curve uniform random variable Choose the appropriate term for each definition below. a probability density curve that (1) extends indefinitely in both directions, approaching, but never touching, the horizontal axis; (2) symmetric about 0; (3) as the number of degrees of freedom becomes larger, it increasingly looks like the standard normal curve a curve that (1) is always on or above the horizontal axis; (2) has the total area between itself and the horizontal axis equal to 1 a probability density curve that (1) starts at 0 on the horizontal axis and extends indefinitely to the right, approaching, but never touching, the horizontal axis; (2) is right skewed; (3) as the number of degrees of freedom becomes larger, it increasingly looks like a normal curve a probability density curve that (1) starts at 0 on the horizontal axis and extends indefinitely to the right, approaching, but never touching, the horizontal axis; (2) is right skewed; (3) possess the reciprocal property a random variable whose probability density function is portrayed as a horizontal line 1/(b-a) above the horizontal axis over the interval from a to For the standard normal variable Z, find the probability P(Z < 1.04) : P(Z < 1.04) = (Round the answer to 4 decimal places) Find the value that divides the area under the standard normal probability density curve into 0.27 to the left and 0.73 to the right. 20.73 (Round the answer to 2 decimal places) Find f0.99 for F distribution with (3,5) degrees of freedom. f0.99 (Round the answer to 2 decimal places) Find t0.001 for T distribution with 5 degrees of freedom. to.001 (Round the answer to 3 decimal places) For X2 ~X 7, use technology to find the probability P(X < 9.54): P(X 0.07): P(T > 0.07) (Round the answer to 4 decimal places) Find t0.6 for T distribution with 77 degrees of freedom. t0.6 (Round the answer to 3 decimal places) For a normal variable X ~ N( = 87.7, = 16.4), find the probability P(X < 110.1) : P(X < 110.1) = (Round the answer to 4 decimal places) For a normal variable X ~ N( = 64.8, = 8.8), find the probability P(54.4 < X < 83.6) : P(54.4 < X < 83.6) = (Round the answer to 4 decimal places) For a normal variable ~ N( = 81.9, = 19.28), find x0.08, the value that divides the area under the density curve into 0.92 to the left and 0.08 to the right. x 0.08 (Round the answer to 2 decimal places) Historically, the SAT score is normally distributed with a mean of 1512 points and a standard deviation of 348.6 points. Let be the SAT score of a randomly selected student. 1. Describe the probability distribution of and state its parameters and : Select an answer ( = , = 2. Find the probability that the SAT score of a randomly selected student is (Round the answer to 4 decimal places) a. less than 2487 points. b. between 1709 and 2318 points. c. more than 2536 points. (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) Select an answer the distribution of the original population is unknown the sample size is large (n>30) although the distribution of the original population is unknown the original population is normally distributed the sample size is small (n 30) although the distribution of the original population is unknown the sample size is small (n