1. Solve for the mean, variance and standard deviation of the following probability distributions. а. 1 2 3 4 P(x) .5 .1 .4 .30 b. 200 000 300 000 |-1 000 000 P(x) .55 .35 .10

A reference states that average daily high temperature in June in a particular city is 86°F with a standard deviation of 7, and it can be assumed that they to follow a normal distribution. We use the following equation to convert "F (Fahrenheit) to "C(Celsius) C-(F-32)=² (a) Write the probability model for the distribution of temperature in C in June in this city. (Round your standard deviation to four decimal places) ~~-[ (b) What is the probability of observing a 31°C (which roughly corresponds to 87.) temperature or higher a a randemily selected day in June in this city? Calculate using the "C model from part (a). (Round your answer to four decimal places.) (c) The probability of observing a 67.8°F temperature or higher on a randomly selected day in June this city is approximately 0.3983, Did you get the same answer or a different answer in part (b)? Are you surprised? Explain. Both sets of calculations produced approximately the same answer which isn't surprising since once we…

A collection of medical scores is Normal with Mean of 50 and Standard Deviation of 10; that is N(50, 10). Bertha’s score is 47.56  and Biff’s score is  56.82.  What is the probability that a randomly selected score will be greater that Bertha’s and less than Biff’s? Your answer should be correct to 4 places after the decimal point.                        ________________

Scores for students on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 108. A random sample of 36 students who took the SAT-I test is selected. Let ?̅ represent the mean score of the sample.   4. The probability that the sample mean score ?̅ is greater than 540 is about (a) 0.9573 (b) 0.5427 (c) 0.6554 (d) 0.0427 (e) 0.17