A metropolitan school system consists of three districts—north, south, and central. The north districtcontains 25% of all students, the south district contains 40%, and the central district contains35%. A minimum-competency test was given to all students; 10% of the north district studentsfailed, 15% of the south district students failed, and 5% of the central district students failed. Develop a probability tree showing all marginal, conditional, and joint probabilities.

• According to data published by the international data security company, Blancco, 27.0% of iPhone 65 devices brought in to mobile carriers and processing companies utilizing Blancco's services between August 1, 2018 and October 30, 2018 were found to have diagnostic issues. If 30 iPhone 6S devices brought in to one of these hundreds of mobile carriers were randomly selected, what is the probability that at least one iPhone 6S will have diagnostic issues?

A large cable company reports that 42% of its customers subscribe to its Internet service, 32% subscribe to its phone service and 23% subscribe to both its Internet service and phone service.  a)  What is the probability that a randomly selected customer subscribes to the Internet service or the phone service?  b)  What percent of customers subscribe to neither the Internet service nor the phone service?

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 58 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 3000 ​batteries, and 1​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

A company that has 150 employees chooses a committee of 11 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use technology to find the number of ways 11 employees can be chosen from 150. (b) Use technology to find the number of ways 11 employees can be chosen from 94 nonminorities. (c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)? (d) Does your answer to (c) indicate that the committee selection is biased? Explain your reasoning. (a) There are 1.49 x 10 16 ways to choose 11 employees from 150 employees. (Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.) 13 (b) There are 6.90x 10 ways to choose 11 employees from 94 nonminorities. (Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.) (c) The…

When purchasing buik orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 47 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 6000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is. (Round to four decimal places as needed.)

The M&M/Mars candy company does a lot of market research to determine the most appealing mix of colors in M&M candies.  Recently, one mix was: Purple 20%; Yellow 20%; Red 20%; Orange 10%; Green 10%; Blue 10% and Brown 10%.  Suppose you reach into a bag of M&M candies and draw out ONE candy at random. What is the likelihood of drawing a Purple candy?

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 48 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 7000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)

Thirty-seven percent of the customers of a grocery store use an express checkout. In a random survey of ten customers: find the expected number (mean) of the number that use express checkout.

2. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (These values ignore a small number of earths among other races. ) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. (a) draw a completely labeled probability tree for this problem. (b) calculate the overall percent of people who died of diabetes across all the three races. (c) given a randomly selected dead person died of diabetes, what is the probability that he/she was white?