The # of flaws in copper wire (X), follows a Poisson Distribution with a rate of 1.5 flaws per mm. What's the probability that there are one or more flaws in 2 mm of wire ?
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- A patient is classified as having gestational diabetes if her glucose level is above 155 milligrams per deciliter (mg/dl) one hour after a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the normal distribution with �=140 mg/dl and �=12 mg/dl. Suppose Sheila repeats this process on three separate randomly selected days. What sample mean blood glucose level is higher than 95% of all other sample mean blood glucose levels? Use 2 decimal places.3) The upper leg length of 20- to 29- year old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm.(3a) What is the probability that a randomly selected 20- to 29- year old male has an upper leg length that is less than 40 cm?(3b) While solving part a, you used a z-score. Describe what you are looking up on Table V at the left & top to find the middle value. You are welcome to use the notation from class that we have used in our notes to show this table location process.(3c) Fill in the result of the work that you have found appropriately into the statement: If we select a simple random sample of n = 100 males ages 20-29, then about ________ of the males would have an upper leg length that is less than 40 cm.The compressive strength of cement samples can be modeled by a normal distribution witha mean of (? + 6000) kilograms per square meter and a standard deviation of (? + 100)kilograms per square meter. Find the probability that a sample’s strength is between(? + 5800) kg/m2and (? + 5900) kg/m2 T = 28 ------------------------------------------------------------------------
- The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 19. Suppose that 42 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65 and 68.6. For the 42 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65 and 68.6. For part b, is the assumption that the distribution is normal necessary? NoYesSuppose that the number of customers who enter a supermarket each hour is normally distributed with a mean of 640 and a standard deviation of 220. The supermarket is open 15 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10500? (Hint: Calculate the average hourly number of customers necessary to exceed 10500 in one 15-hour day.) probability= ?A particular fruit's weights are normally distributed, with a mean of 785 grams and a standard deviation of 9 grams.If you pick 13 fruit at random, what is the probability that their mean weight will be between 783 grams and 791 gramsRound to 4 decimal places
- A particular fruit's weights are normally distributed, with a mean of 462 grams and a standard deviation of 22 grams.If you pick 23 fruit at random, what is the probability that their mean weight will be between 446 grams and 477 gramsRound to 4 decimal places, as needed.What is the probability that the part lasts less than 1 hour?Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
- ALICE and YouGov conducted an online poll among Americans hotel guests of more than 18 years old to understand their expectations from hotels in the year 2018-191. This poll showed that 40% of guests were interested in gaining experiences of local cuisine tastings/tours. Suppose you take a random sample of 10 hotel guests. Let, x, represent the number of guests interested in gaining experiences of local cuisine tastings/tours. Find the mean and standard deviation of x. What is the probability that x <=5? Find the probability that x > 7.The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
