A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(x)=\left\{\begin{array}{ll} 0 & x<0 \\ 0.02 & 0 \leq x<1 \\ 0.18 & 1 \leq x<2 \\ 0.35 & 2 \leq x<3 \\ 0.65 & 3 \leq x<4 \\ 0.85 & 4 \leq x<5 \\ 0.98 & 5 \leq x<6 \\ 1 & 6 \leq x \end{array}\right. Calculate the following probabilities directly from the cdf: (a) P(2), that is, P(X = 2) (b) P(X > 3) (c) P(2 S X s 5) (d) P(2 < x < 5)

-When written out in full, the number (102020 + 2020)² has 4041 digits. What is the sum of the digits of this 404 1-digit number? А 9 В 17 С 25 D 2048 E 4041

The pitcher's mound on a women's softball field is 43 feet from home plate and the distance between the bases is 60 feet, as shown in the diagram below. (The pitcher's mound is not halfway between home plate and second base.) How far is the pitcher's mound from first base?

\left\{\begin{array}{l} y=7-x \\ x+3 y=7 \end{array}\right. \left\{\begin{array}{l} 4 x+3 y=-16 \\ -x+y=4 \end{array}\right. \left\{\begin{array}{l} 2 x-4 y=-4 \\ 3 x-y=4 \end{array}\right.

A rivet is to be inserted into a hole. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.00X millimeters. (a) Construct a 99% two-bounds confidence interval for o2. (b) Construct a 99% lower confidence bound for o.

The Foster family wants to save money to travel the world. They purchase an annuity with a quarterly payment of $139 that earns 4.7% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 13 years. Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

A computer consulting firm presently has bids out on three projects. Let A, = {awarded project ), for i 1, 2, 3, and suppose that P(A,) = 0.22,P(A2) = 0.25, P(A,) 0.28, P(A,n A2) = 0.12, P(A, n A3) = 0.03, P(A, n Ag) = 0.05, P(A, n A, n Ag) = 0.01. Express in words each of the following events, and compute the probability of each event. (a) A1 U A2 Express in words the event. *awarded only 1 *awarded only 2 *awarded neither 1 nor 2 *awarded either 1 or 2 *awarded either 1 or 2 (or both) Compute the probability of this event. (b) A,'n A, [Hint: (A, U A,)' = A,'n A2] Express in words the event. *awarded only 1 *awarded only 2 *awarded neither 1 nor 2 *awarded either 1 or 2 *awarded either 1 or 2 (or both) Compute the probability of this event.

(1 point) Suppose S = {r, u, d} is a set of linearly independent vectors. If x = 3r + 2u + 3d, determine whether T = {r, u, x} is a linearly independent set. 1. Is T linearly independent or dependent? If T is dependent, enter a non-trivial linear relation below. Otherwise, enter 0's for the coefficients. ________r+_________u+______x = 0.

The life in hours of a 75-watt light bulb is known to be normally distributed with o = 24hours. A random sample of 25 bulbs has a mean life of x = 1500 hours. (a) Construct a 9X% two-bounds sided confidence interval on the mean life. (b) Construct a 9X% lower confidence bound on the mean life. (c) Construct a 95% upper confidence bound on the mean life. (d) Find the sample size such that the maximum error (E) in both sides is 2 hours

3) In a survey, 46,281 women were asked how many children they had. The results were as follows. a) P(Sampled woman has exactly 4 children)? b) P(Sampled woman has more than 3 children)? c) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than seven children. d) Using a cutoff of 0.05, is it unusual for a woman in the survey to have no children?