There is a normal distribution with mean 10 and standard deviation of 8. What is the probability of selecting a value less than 15? Round every step to 2 decimal points.
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- A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation of 44 ounces. What is the probability of filling a cup between 21 and 31 ounces? Round your answer to four decimal places.Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impurities per bag are normally distributed with a mean of 12.2 grams and a standard deviation of 2.8 grams. A bag is chosen at random.a. What is the probability that it contains less than 10 grams of impurities?b. What is the probability that it contains more than 15 grams of impurities?c. What is the probability that it contains between 12 and 15 grams of impurities?d. It is possible, without doing the detailed calculations, to deduce which of the answers to parts (a) and (b) will be the larger. How would you do this?Beer bottles are filled so that they contain an average of 330 ml of beer in each bottle. The amount of beer in a bottle is normally distributed with a standard deviation of 2.9 ml. 21 What is the probability that a randomly selected 6-pack of beer will have a mean amount in 6 bottles less than 328ml? a 0.0292 b 0.0365 c 0.0456 d 0.0570
- According to AAA, the price of a gallon of regular, unleaded gas across gas stations in North Carolina is normally distributed with a mean of $2.39 and a standard deviation of $0.15. Find the price such that the probability that a randomly chosen gas station charges more than that price is 5%. Group of answer choices $2.14 $2.39 $2.52 $2.64 thanksA small retail store has customers whose ages are normally distributed, with a mean of 37.5 and a standard deviation of 7.6. What is the probability that a randomly selected customer is younger than 25 years old? Round your answer to three decimal places, e.g. 0.685.The mean cost of domestic airfares in the United States rose to an all-time high of $395 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $115. Use Table 1 in Appendix B. a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $300 and $490 (to 4 decimals)? d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)
- Suppose commute times in a large city are normally distributed and that 65.20% of commuters in this city take more than 22 minutes to commute one-way. If the standard deviation of such commutes is 6.5 minutes, what is the mean commute?Home prices in a particular neighborhood average $350k with a standard deviation of $30k. They are not Normally distributed. Your realtor pulls a random sample of 30 houses for you to look at. What is the probability that the average price of these 30 houses is more than $345k? (Please round your answer to 3 decimal places: ex, 0.123)The diameters of ball bearings are distributed normally. The mean diameter is 99 millimeters and the standard deviation is 5 millimeters. Find the probability that the diameter of a selected bearing is greater than 109 millimeters. Round your answer to four decimal places.
- Given that u = 10 and σ = 5, fill in the following probability statement if we are trying to find the probability that x is within 2 standard deviations of the mean. P ...≤ x ≤.....A NUMMI assembly line, which has been operating since 1984, builds 900 cars and trucks in a week. Generally, 10% of those cars are defective coming off the assembly line. What type of distribution does the event of having defective cars follow? What are the mean and standard deviation of this random event? (6 points) Can we apply the normal distribution to study this event? Check the conditions and answer the question. (6 points) Find the probability that the assembly line produces at least 825 cars, that are not defective and functional, in a week. Graph the situation, shade in the area to be determined, and find the probability. (6 points)Assume that the traffic to the web site of Smiley’s People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.48 million visitors per day and a standard deviation of 800,000 visitors per day. (a) What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits. (b) What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits. (c) What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits. (d) Assume that 85% of the time, the Smiley’s People web servers can handle the daily web traffic volume without purchasing additional server capacity. What is the amount of web traffic that will require Smiley’s People to purchase additional server capacity? If needed, round your…