Anuja is at the bottom left (0, 0) of a coordinate grid of size n ∗ m, and she can only move right and up unit distance along the edges (She cannot move towards the right and above of the point (n, m)). She chooses a path randomly and every path is equally likely. What is the probability that she passes through a point (x, y) in her path? (x>=0 and x<=n and y>=0 and y<=m)

Let Q,, Q2 and Q, be dummy variables with the value 1 indicating observations are from first, second and third quarters and the value 0 otherwise, respectively. If the investigator estimates company sale measured in million dollars as sale = 4+ 20, +2.5Q2 +30,, then the investigator: O a. forecasts sale for the first quarter to be 3.5 m$. O b. forecasts sale for the first quarter to be 3 m$. O c. forecasts sale for the first quarter to be 1 m$. O d. forecasts sale for the last quarter to be 8.5 m$. e. forecasts sale for the last quarter to be 4 m$.

A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. T.... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, than 0.05. It be unusual to observe two components fail, since the probability that two components fail,, is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) O Time Remaining: 02:29:14 Next Left Raht