=1Assume that the random variable X is normally distributed, with mean = 50 and standard deviation σ = 11. Compute the probability. Be sure to draw a normal curve with the areacorresponding to the probability shaded.P(X ≤47)Which of the following shaded regions corresponds to P(X ≤ 47)?OA.4750XEP(X ≤47)=IN(Round to four decimal places as needed.)OB.C.47504750

The mean and standard deviation of random variable X are 50 and 11 respectively.

Answered: Assume that the random variable X is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.If 4% of the thermometers are rejected because they have readings that are too high and another 4% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. Round answers to 3 decimal places.interval of acceptable thermometer readings Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P5, the 5-percentile. This is the temperature reading separating the bottom 5% from the top 95%.P5 = °C Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.A single…
Suppose that time spent by a group of people on social media follows anormal distribution with a mean of 75 minutes and a standard deviation of 10 minutes. a) What is the probability that a person selected at random spends morethan 60 minutes on social media? b) Of the people, 95% spend less than Th minutes on social media. Find thevalue of Th. c) As you have learned in the lecture, a normally distributed random variable also takes negative values as it is defined over (-∞,+∞). Why do many random variables that take only positive values, like the one in this question, can still be assumed to have a normal distribution?
Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.If 4.1% of the thermometers are rejected because they have readings that are too high and another 4.1% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.interval of acceptable thermometer readings = _________ °C
The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 385. Assume this mileage follows the normal distribution with a standard deviation of 31 miles. What is the probability that, before the low-fuel light comes on, the car will travel exactly 359 miles on the next tank of gas? Note that there in no area under a curve at a specific value. That is, if you think of a rectangle as the area under the curve, the width would be zero and so the area would be zero. With this information, find the probability.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.If 4.7% of the thermometers are rejected because they have readings that are too high and another 4.7% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.Interval of acceptable thermometer readings _________ °CEnter your answer as an interval (a,b) with 2-decimal place accuracy.
The amount of wear on a shaft (0.0001 in) after a fixed mileage was determined for each of n = 8 internal combustion engines with lead-copper bearings and obtained = 3.72 and s = 1.25. (a) Assuming that the shaft wear distribution is normal with mean μ, use the test at the 0.05 level to test H0: μ = 3.50 against H1: μ > 3.50. (b) With σ = 1.25, what is the probability of type II error (β) of the test if the alternative were μ = 4.00? Note:The exercise in the image is in Spanish, to make the exercise more understandable.
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8584 g and a standard deviation of 0.0517g. A sample of these candies came from a package containing 467 candies, and the package label stated that the net weight is 398.6g. (If every package has 467 candies, the mean weight of the candies must exceed StartFraction 398.6 Over 467 EndFraction equals 0.8536g for the net contents to weigh at least 398.6g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8536g. The probability is (Round to four decimal places as needed.) b. If 467 candies are randomly selected, find the probability that their mean weight is at least 0.8536g. The probability that a sample of 467 candies will have a mean of 0.8536 g or greater is (Round to four decimal places as needed.)
An airliner carries 300passengers and has doors with a height of 70in. Heights of men are normally distributed with a mean of 69.0in and a standard deviation of 2.8 in. a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is _____. (Round to four decimal places as needed.) b. If half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 70 in. The probability is ____. (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? A. The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend. B. The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male…

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