Find the variance and standard deviation of X
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The random variable X representing the number of errors per 100 lines of software code, has the following probability distribution:
| x | 2 | 3 | 4 | 5 | 6 |
| PX(x) | 0.01 | 0.25 | 0.4 | 0.3 | 0.04 |
Find the variance and standard deviation of X
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- Assume that adults have IQ scores that are normally distributed with a mean of 98.1 and a standard deviation of 17.5 find the probability that a randomly selected adult has an IQ greater than 127.5.A psychopathologist records the number of criminal offenses among teenage drug users in a nationwide sample of 1,201 participants. To measure the variance of criminal offenses, he computes SS = 10,800 for t his sample. Compute the standard deviation.The green turtle migrates across the Southern Atlantic in the winter, swimming great distances. A study found that the mean migration distance was 2,200 kilometers and the standard deviation was 625 kilometers. Assume that the distances are normally distributed. Find the probability that a randomly selected green turtle migrates a between 1,900 kilometers and 2,200 kilometers.
- A random variable X is normally distributed with mean = 80 and standard deviation = 4.5. What is the probability that X is less than 75.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?Scenario: Suppose a financial institution holds a well diversified $35,500,000 position in stocks. The variance of this position in relation to the overall S&P is equal to 1.95. Over the past year the average daily variation of the S&P is 160 basis points with a standard deviátion of 80 basis points. The z-score is 1.96. What is the stock value change that corresponds to a 95% probability that no stock changes will exceed this value? O 162.574 basis points 465.76 basis points 132 basis points O 292 basis points
- According to a poll, individuals keep their mobile phones for an average of 1.4 years before purchasing a new one. The standard deviation for the year is 0.24 year. A mobile phone user is chosen at random. Determine the likelihood that the user will keep their existing phone for less than a year before purchasing a new one. Assume that the variable x has a regularly distributed distribution.The mean time for a group of adults to complete a certain achievement test is 38.8 minutes and the standard deviation is 7 minutes. Assume the variable is normally distributed, find the probability that the mean of 50 randomly selected adults finished the test in less than 35 minutes? The mean time for a group of adults to complete a certain achievement test is 38.8 minutes and the standard deviation is 7 minutes. Assume the variable is normally distributed, find the probability that the mean of 50 randomly selected adults finished the test in less than 35 minutes? 6.19 x 10-5 0.2936 0.7064 0.9999The 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
- A speed camera on Peterson Road records the speed of each passing vehicle. The speeds are found to be normally distributed with a mean of 67 km h and a standard deviation of 3.8 km h-1. A vehicle on Peterson Road is chosen at random. Find the probability that the speed of this vehicle is (i) more than 60 km h¯1; (ii) less than 70 km h-1;Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability of randomly selected adult has an IQ score less than 115.Calculate the expected value, the variance, and standard deviation where X is the number of tails that come up when a coin is tossed three times
