The probability of a war in the international system is...

The probability of a war in the international system is normally distributed with a mean of 15 and a standard deviation of 8. How far are the following scores, in standard deviation units, from the population mean and give a one sentence interpretation of each result, i.e., what it means? Calculate the probabilities associated with each of the following raw scores: 8) the probability of observing 12 wars or less: 9) The probability of observing between 12 and 17 wars 10) The probability of observing 13 wars or more: 11) The probability of observing between 10.5 and 14 wars: 12) The probability of observing more than 16 wars or less than 14 wars:

Transcript

00:01 Hello everyone we are going to solve a question in this question we are given the mean we are given mean mu is equals to 15 standard deviation standard deviation that is sigma is equals to 8 and in a part we have to find probability that x is less than 12 so for solving this we have probability x less than 12 is equal to probability x minus mu divided by sigma is less than 12 minus 15 divided by 8 and from here we have probability that z is less than minus 3 divided by 8 so from z score table this value is equal to 0 .3538 this is the answer of a part of the question moving towards the b part of the question in this we have to tell probability that x lies between 12 and 17.

01:04 So for this probability that x lies between this is equal to probability x lies between 12 and 17 is equals to probability 12 minus 15 divided by 8 is less than x minus mu divided by sigma is less than 17 minus 15 divided by 8 and from here we have this is equals to probability minus 3 divided by 8 is less than z less than to here we have 1 divided by 4 and by applying the formula of probability this is probability z less than 1 divided by 4 minus probability z less than minus 3 divided by 8 and from z go table this is equals to 0 .2449 which is the final answer of second part of the question moving towards the c part of this question in this we have to find the probability that x is greater than 13 so for finding this probability probability probability that x is greater than 13 is equals to 1 minus probability date x is less than 13.

02:10 Now by applying the formula this is equals to 1 minus probability x minus mu divided by sigma is less than 13 minus 15 divided by 8.

02:21 And on finding this we have this is equal to 1 minus probability z less than minus 1 divided by 4.

02:29 So this value is equals to 0 .5987, which is the final answer for c part of the question.

02:37 Now moving towards the d part of the question, in d part we have to find probability that x is between 10 .5 and 14...

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