A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P(1.5
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- A normal distribution has a mean of u= 28 and o= 4. If one score is randomly selected from the distribution, what is probability that the score will be less than X=23?Assume the random variable X is normally distributed, with mean μ=55 and standard deviation σ=4. Find the 6th percentile.The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 5.95 ounces and a standard deviation of 0.14 ounce. Suppose that you draw a random sample of 32 cans. Find the probability that the mean weight of the sample is less than 5.9 ounces. Probability = xxxxxxxxxxxx
- Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. Find the probability that the reading is between 1.5°C and 1.71°C.A random variable has a longnormal distribution with mean 10 and variance 4. Calculate the probability that the variable will take a value between 7.5 and 12.5Let x be a random variable that represents the commute time of teachers in a large rural area. If x is normally distributed with a mean of 64 minutes and a standard deviation of 12.2 minutes, find the probability that a commute time is greater than 70 minutes.
- The random variable X has a uniform distribution with values between 15 and 25. What is the mean and standard deviation of X?Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that X is less than 9.66 is 0.67, then what is the standard deviation of X?A normally distributed random variable has a mean of 449. If a score of 433 lies two standard deviations below the mean, find the variance of X.
- The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, find the mean and standard deviation of the number of recoveries among 15 patients.Assume the random variable X is normally distributed with mean =50 and standard deviation =7. Compute the probability. P(X > 36)=