Let x be a continuous random variable that is normally distributed with a mean of 60 and a standard deviation of 9. Find the probability that x assumes a value between 55 to 75
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Question 1
Let x be a continuous random variable that is
standard deviation of 9. Find the
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- On a test of spatial reasoning, it is found that scores for men follow a normal distribution with mean mu = 200 and standard deviation sigma = 60 Scores for women also follow a normal distribution, but with mu = 180 and sigma = 20 What percentage of men's scores fall between 200 and 305 in the distribution (Round your answer to 2 decimal places . What is the probability that a randomly selected woman will have a score greater than 200? (Include 4 decimal places in your answer.) Suppose individuals who score in the top 5% of the distribution for their gender are eligible to receive a scholarship to a prestigious architecture program . What score would be needed for a man to earn this scholarship ? What score would be needed for a woman to earn the scholarship (described in previous question ) ? Would a score of 250 on this test be a better score for a man or a woman Explain your answer to the previous question. How did you arrive at your decision?Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in 224 to 236 minutes? Round your answer to four decimal places. iThe mean total cholesterol for a population of men between the ages of 20 and 29 is 180 micrograms per decilitre with a standard deviation of 37.4. A healthy total cholesterol level is less than 200, 200-240 is border line, and above 240 is dangerous. Assume the distribution is approximately Normal. For a randomly selected man from this group, what is the probability that his total cholesterol level is i. 200 or more? 1i. Between 200 and 240?
- A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100. A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15. Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance? Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and whyThe life of light bulbs is distributed normally. The standard deviation of the lifetime is 26 hours and the mean lifetime of a bulb is 570. Find the probability of a bulb lasting for at least 603 hours (Round your answer to four decimal places) CS Scanned with CamScannerI'm having a hard time on this question. A single toss of a fair coin results in either 0 or 1 head, each with probability 1/2. Define H = number of heads obtained on a single toss. The mean of H is = 0.5 And the standard deviation of H is = 0.5. Suppose you toss a fair coin four times. Define T = total number of heads obtained. Find the mean and standard deviation of T.
- The amounts of sugar in a serving of children's breakfast cereals is normally distributed with a mean of 8.4 grams and a standard deviation of 2.1 grams. For a sample of 15 children's breakfast cereals, what is the probability that the sample mean amount of sugar in a serving for the 15 cereals will be at least than 10 grams? Show how you calculated your result here (type in what you typed on your calculator or computer, the function used on the calculator/computer with value input, etc) Calculation: ___________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(x¯<10 grams) = ___________The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places.Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…
- The test score of a physics class with 160 students is distributed normally with a mean of 75 and standard deviation of 7. what percentage of the class has a test score between 68 and 82 Approximately how many students have a test score between 61 and 89? What is the probability that a student chosen at random has a test score between 54 and 75? Approximately how many students have a test score greater than or equal 96?Assume that IQ scores of Red Sox fans are normally distributed with the mean of 63.6 in a standard deviation of 2.5 if 90 Red Sox fans are randomly selected by the probability that they have a mean IQ score of 62.9 and 64.D = 129 , E = 56 , F = 134