what is the probability that, at the end of a period, at least 88 components are working
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A system is made up of 100 components, each of which has a reliability (
context, what is the probability that, at the end of a period, at least 88 components are working? (Do not use continuity correction in the approximation of the Binomial distribution by the
Let , X be the number of components are working
Here , X→B(n=100 , p=0.9)
The probability mass function of X is ,
; x=0,1,2,.......,n and q=1-p
= 0 ; otherwise
Our aim is to find the probability that, at the end of a period, at least 88 components are working.
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- Suppose that 16% of the U.S. population is left handed. If a random sample of 130 people are selected, approximate the probability that fewer than 23 are left handed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to three decimal places but do not round intermediate steps.Suppose that half of all students (50%) in campus dormitories are dissatisfied with the food service. A random sample of 64 students was taken. What is the probability that the number of students in the sample who were dissatisfied with the food service was between 30 and 34 (inclusive)? (Use the normal approximation to the binomial distribution, without the continuity correction.).8% of all cars fail the emissions inspection, find the probability that in a sample of 85 cars, 11 will fail. Use the Poisson approximation to Find the mean number λ of cars that fail the emissions inspection in a sample of 85 cars.
- The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 63.5%. What is the probability that in a random sample of 440 headache sufferers, no more than 256 obtain relief? Remember to use the continuity correction and calculate z-scores to at least 3 decimal places. Give probabilities to 4 decimal placesAccording to an SSA study, around 32% of 65-year old women will live to at least 90. An insurance company has a part of its portfolio made of life insurance policies sold to 65-year old women. Based on the SSA study the insurance company expects that 68% of 65-year old women will pass away before reaching the age of 90. A simple random sample of 200 is taken. Use the normal approximation along with the continuity correction factor to find the probability that at least 140 women in the sample will pass away before reaching the age of 90. • Let X be the number of females out of 200 that pass away before reaching the age of 90. Describe the distribution of X and its parameters: X Select an answer (n= Use the random variable notation to symbolically express the probability that at least 140 females out of 200 pass away before reaching the age of 90: Select an answer • Let Y be a normal variable that will be used to approximate the probability in question. Find the parameters of Y (round…
- Suppose that 15% of the population of the chips are defective. If a random sample of 250 chips from the box is chosen, approximate the probability that fewer than 30 are defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to four decimal places.Suppose that 12% of the population of the U.S. is left-handed. If a random sample of 190 people from the U.S. is chosen, approximate the probability that at most 24 are left-handed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.It is known that the average lifetime of a central processing unit (CPU) of a server is eight years and shows an exponential distribution. What is the probability that the company that leases the server for five years will encounter a central processing unit (CPU) failure within the lifetime? a)0.465 b)0.395 c)0.535 d)0.606 e)no one
- Need helpTwo movie theaters compete for the business of 1,000 customers. Assume that each customer chooses between the movie theaters independently and with "indifference." Let N denote the number of seats in each theater. (a) Using a binomial model, find an expression for N that will guarantee that the probability of turning away a customer (because of a full house) is less than 1%. (b) Use the normal approximation to get a numerical value for N.According to recent data, 45% of the U. S. adults have hypertension. A random sample of 750 adults in the U.S. is selected. Let X represent the number that have hypertension. a. Under what condition will this binomial distribution be bell-shaped? State this condition and verify that that condition is met here. Show the calculation required.
