(a) If a shaft is selected at random, what is the probability that the shaft conforms to surface finish requirements or to roundness requirements or is from Tool 1? (b) If a shaft is selected at random, what is the probability that the shaft conforms to surface finish requirements or does not conform to roundness requirements or is from Tool 2?
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- Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 36 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,760 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is 5,760 lb = 160 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normall 36 distributed with a mean of 182.6 lb and a standard deviation of 37.4. greater than The probability is approximately. (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? O A. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft. B. No. Because the probability is high, the aircraft is safe…The expected life of a certain component in a mechanism is treated as a random variable having a gamma distribution with a = 3 and ß = 2. The average expected life of such component is 12 months, what is the probability that this component can have a greater than average expected life?6) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability less than 2.22. 7) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability greater than 3.28. 8) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability between -1.00 and -2.50.
- 13. Machine components are mass-produced at a factory. A customer requires that the components should be 5.200cm long but they will be acceptable if they are within limits 5.195cm to 5.205cm. The customer tests the components and finds that 11.75% of those supplied are over-size and 5.95% are under-size. Assuming components supplied are normally distributed. What is the probability that one is under-size, one is over-size and one satisfactory given three of the components are selected at random? In a survey into working practices, the distance walked each day by a postal worker delivering mail in a residential district was recorded. For each weekday (Monday to Friday) the distribution had mean 12km and standard deviation 0.9km. For Saturdays the distribution had mean 10km and standard deviation 0.5km. No mail was delivered on Sundays. The distances walked on different days may be assumed to be independent of each other and normally distributed. Use this information to answer…Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 35 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,880 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,880 lb = 168 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.8 lb and a standard deviation of 35 35.3. ...... The probability is approximately. (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? O A. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft. O B. No. Because the probability is high, the aircraft…
- A company manufactures two types of cables, brand R and brand Q. Brand R has mean breaking strengthof 4500kg with a standard deviation 400kg, while brand Q have mean breaking strength of 4800kg with astandard deviation 200kg.i) What is the probability the mean breaking strength brand R is less than 4890kg?ii) What is the probability the difference breaking strength between these two brands is greater than200kg?iii) If 80 cables of brand R and 70 cables of brand Q are tested, what is the probability that the samplemean of breaking strength brand Q is better than brand R?Q4 For the tornado events in a certain region, the tornado-induced wind speed can be modeled by a lognormal random variable with a mean value of ux = 120 mph and a standard deviation of ox = 12 mph. a) Calculate the probability that the wind speed will be between 100 mph and 130 mph in a tornado event. b) If a structure located in this region is designed to resist for wind speed of 150 mph, what is the probability that the structure will be damaged during such a tornado?A certain model of an automobile is having a fault in the braking mechanism after sale. This is a very serious failure with catastrophic results at high speed. The distribution of the number of cars per year that will experience the fault is found to be a random variable with x=5. a) What is the probability that at most 3 cars per year will experience a catastrophe ? b) What is the probability that more than 1 car per year will experience a catastrophe ?
- A Engr. Juan dela Cruz is in-charged of ensuring the quality of products and services produced by their beverage company located in Southern Luzon. One of their products is bottled cranberry juice. He observed that the amount of juice drink in each 32 mL bottle is actually a normally distributed random variable, with a mean of 32.2 mL and a standard deviation of 0.3 mL. a) Find the probability that, if a customer buys one bottle will contain less than 32 mL. b) Find the probability that, if a customer buys a cartoon of four bottles, the mean of the four will be less than that of 32 mL.The probability that the weather will be sunny tomorrow is 0.73. What is the probabilitv that the weather will NoT be sunny tomorrow?a) The number of calls coming per minute into a hotels' reservation center is Poisson rand variable with mean 3. (i) Find the probability that no calls come in a given minute period. (ii) Find the probability that no calls come in a given half a minute period. b) Su