Use R to find the following probabilities: a) Pr{Z < 4.05} b) Pr{Z > -0.75} c) Pr{-1.35 < Z < 1.35} d) Pr{-1.8 < Z < 1.1} e) Pr{Z < -1.35 or Z > 1.35} (you want the probability outside the range -2.67 to 2.67)

Find the following probabilities, where z∼n(0,1) a.p (−1.67≤ z ≤1.44) b.p (z>1.98)

According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let Y = the number of days on which the train arrives on time. What is P(Y = 4)? Interpret this value. (0.90)4 (0.10)². There is a 0.66% probability that exactly 4 of the 6 trains arrive on time. (0.90) ¹ (0.10)². There is a 0.66% probability that at least 4 of the 6 trains arrive on time. This probability cannot be calculated because this is not a binomial setting. O()(0.90)+ (0.10)². There is a 9.84% probability that at least 4 of the 6 trains arrive on time. O()(0.90)4 (0.10)². There is a 9.84% probability that exactly 4 of the 6 trains arrive on time.

The following table lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at a local hospital Use the table to find the following probabilities a)P( X=1) b)P(X ≥3) c)P(X <2)

1) Assuming 6 degrees of freedom, find the following probability. P(T > 1.7) = 2) Assuming 16 degrees of freedom, find the following probability. P(T < – 2.024) =

Using historical records, the personnel manager of a plant has determined the probability of X, the number of employees absent per day. It is 2 4 6 7 P(X) 0.005 0.0246 0.31 0.33910.2195 0.080.01850.0033 4. Find the following probabilities. Be sure to give your answer to 4 decimal places. A. P(2 5) Probability = С. Р(Х < 4) Probability: %3D 出

A manufacturer of plumbing fixtures has developed a new type of washerless faucet. Let p = P(a randomly selected faucet of this type will develop a leak within 2 years under normal use). The manufacturer has decided to proceed with production unless it can be determined that p is too large; the borderline acceptable value of p is specified as 0.10. The manufacturer decides to subject n of these faucets to accelerated testing (approximating 2 years of normal use). With X = the number among the n faucets that leak before the test concludes, production will commence unless the observed X is too large. It is decided that if p = 0.10, the probability of not proceeding should be at most 0.10, whereas if p = 0.30 the probability of proceeding should be at most 0.10. (Assume the rejection region takes the form reject H, if X 2 c for some c. Round your answers to three decimal places.) What are the error probabilities for n = 10? n USE SALT P-value = 0.07 B(0.3) =

Use the tables provided to give your best estimate to the 6. probabilities: а. Р(Z> 1.9) b. P(ti, >1.9) c. P(Xs > 42.1) d. P(F,14 >1.8)

The percentage of vehicles on a freeway that violate the speed limit is π = 0.88 You randomly clock  n = 80  vehicles.   32)   The probability that between  66 and 70 vehicles violate the speed limit is   P(66 ≤ x ≤ 70) =                 a 0.4350 b 0.4438 c 0.4529 d 0.4621

Pavan