Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 84% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 32% of all defective components. What is the probability that the following occur? (a) A defective component will be detected only by the first inspector? 0.1344 × A defective component will be detected by exactly one of the two inspectors? 0.2688 × (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)? 0.032768

If you randomly select five peanut M&M’s, find the probability that none of them are yellow.

A commercial for a manufacturer of household appliances claims that only 3% of all its products require a service call in the first year. A consumer protection association wants to check this claim and so surveys 400 households that recently purchased one of the company's appliances. What is the probability that there is a difference of at most 0.4% between the sampled proportion of appliances that require a service call within the first year and the proportion claimed by the manufacturer? 00.68 00.47 00.36 00.01 00.32 What is the probability that more than 97% of the sample appliances do not require a service call within the first year? O None of the other options give the correct probability. 0 1 0.03

Dispatches to the Miami Coast Guard Search & Rescue Division concern either routine or emergency cases. The time to process a routine case is an exponential random variable with an expected value of 3 minutes, while the time to process an emergency case is an exponential random variable with an expected value of 10 minutes. A dispatch is routine with a probability of 0.8, or an emergency with a probability of 0.2. The status of dispatches and processing times are independent across dispatches. Let X be the processing time of the next dispatch. a) Calculate P{X > 4}.b) Calculate E[X].c) Calculate Var(X). (Hint: Var(X) = E[Var(X |Y )] + Var(E[X |Y ]).

The lifespan of a car battery is normally distributed with μ = 5 years and o= 1.2 years. What is the probability that a new battery will last between 7 and 8 year 4.16% 13.74% 2.15% 3.61% New version available! (3.0.286) GET IT NOW

-A certain manufactured part must be scrapped if it is defective. Currently, at your manufacturing facility, 11% of those parts are defective. Find the probability of more than one defective part in a random batch of 26 parts. (Show 2 decimal places.)

15%0f cellphone users use their cell phones to access internet. In arandom sample of 10 cellphone users, what is probability that exactly 2 have used their phones to access internet?

Q7 (a) 2% of customers at the snack counter of a movie theater buy soft drinks. Among those who buy soft drinks, 53% also purchase popcorn. (i) What is the probability that a customer at the counter buys a drink and popcorn? Theaters use this type of calculation to decide which products should be bundled to appeal to Based on the probability so calculated, what is your recommendation customers. Whether to bundle the products or not? (ii) If the proportion of customer who buys popcorn 68% . Then find the probability that a customer will buy a popcorn or a soft drink?

In a certain town, 62% of the residents enjoy riding roller coasters. Alfred takes a sample of 75 residents from this town. What is the probability that fewer than 58% of the residents in the sample enjoy riding roller coasters? 0.238 0.433 0.714 0.762

Suppose the probability of success in a binomial trial is 0.63. What is the probability of failure? OA. 0.77 OB. 0.23 O C. 0.63 O D. 0.37