if X is normally distributed withe mean 10 and standard deviation 2, what is the probability that X is less than 5?
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if X is
Given,
X is normally distributed with mean µ=10 and standard deviation σ=2.
i.e. X~N (10,2)
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- 3. Let Y,,. , Y, be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?6. Oranges chosen at random have a mean mass of 210 grams and standard deviation of 35 grams. Assuming a normal distribution, what is the probability of choosing an orange with a mass between 170 grams and 250 grams?The waiting time to get food at a fast-food restaurant is 4.7 minutes on average with standard deviation of 2.5 munutes. Suppose that a sample of 32 customers is randomly selected. A. What are the mean and standard deviation of the sample mean waiting time of 32 customers? Mean = Standard Deviation (standard error of the mean) minutes minutes Round standard error to 5 decimal places. B. What is the probability that the average waiting time of 32 customers is less than 4.4 minutes? Round to 4 decimal places. C. What is the probability that the average waiting time of 32 customers is greater than 4.8 minutes? Round to 4 decimal places. D. What is the probability that the average waiting time of 32 customers is between 4.4 and 4.8 minutes? Answer: Answer:
- Suppose that X is normally distributed with mean 85 and standard deviation 15. A. What is the probability that X is greater than 107.5? Probability = B. What value of X does only the top 16% exceed? X =It is known that the mean weight of students at cavendish university is 72 kg with a standard deviation of 3 kg. What would be the probability of finding individuals with weights between 74kg and 78 kg? ( Assume weight to be normally distributed).It is known that the mean weight of student at Cavendish University is 72 kg with a standard deviation of 5 kg. What would be the probability of finding individuals with weights less than 705 kg? ( Assume weight to be normally distributed)
- Suppose X is a random variable with mean 16 and standard deviation 4 which follows normal distribution. Find the probability that x is less than 18? Round your answer to four decimalsSuppose speeds of vehicles traveling on a highway have an unknown distribution with mean 63 and standard deviation 4 miles per hour. A sample of size n=34 is randomly taken from the population and the mean is taken. What is the probability that the sample mean is less than 65 mph? Do not round your answer.A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.3 years, and standard deviation of 1.3 years.If you randomly purchase 4 items, what is the probability that their mean life will be longer than 6 years?
- If our population follows a normal distribution with mean 50 and standard deviation 3, then what is the z-value for calculating the probability of observing a value of less than 47 in this population?Suppose that X is a normally distributed with a mean 23 and standard deviation is 6 find the given probability, P(X<26) Round to four decimalsA sample of size 14 will be drawn from a population with mean 100 and standard deviation 40. Is it appropriate to use the normal distribution to find probabilities for x? Yes O No X
