Q2 (5 points) If X is a normal random variable with...

Q2 (5 points) If X is a normal random variable with parameters $\mu = 10$ and $\sigma^2 = 36$, compute (a) $P(X > 5)$ (b) $P(4 < X < 16)$ (c) $P(X < 8)$ (d) $P(X < 20)$ (e) $P(X > 16)$

Transcript

00:01 So in this question, if x is a normal random variable with parameters, mu is equal to 10, mu represents the mean value, and the sigma square is the variance which is equal to 36.

00:13 We need to calculate the probability when p of x is greater than equal to 5, p is 4 less than x less than 16, p of x less than 8 and p of x less than 20 and p of x greater than equal to 16.

00:26 These are the five cases that we need to calculate the probability here so these are the normal distribution these all these things follows the normal distribution here so first i will calculate the probability of x greater than 5 so i need to rewrite this probability in terms of z so that we can calculate the value of this probability so i'm going to write this as p of x minus mu my sigma greater than 5 minus mu value is 10 by sigma is sigma is under root of 36 sigma is equal to 6 so p of x minus mu of sigma is written as is also written as z value so z is a standard score value used in the normal distribution curves so z is greater than equal to 0 .m.

01:28 Minus 0 .83 5 minus n by 6 is equal to minus 0 .83.

01:33 So we need to calculate this probability value as the z score is given to us here, but we need to rewrite it in terms of z less than symbol.

01:44 So we'll retry to add up 1 minus probability of z less than minus 0 .83.

01:50 So we need to calculate the probability of where z is 0 .83.

01:55 So here i need to calculate the probability when z value is 0 .83.

01:59 So here i need to calculate the probability when z value is is minus 0 .83 so for that we have two methods to calculate the value of z is equal to minus 0 .83 one is the using the normal distribution tables normal distribution tables these are the standard values which gives the probability value when we where when we have the z score value and another is using the ms excel sheets so here i'm going to find out using the two methods, but later on for the remaining problems, i'm going to directly write the values here.

02:43 So from the table of the standard distribution in the first column, locate the first two digits of the z value.

02:49 So what is the first two days? it is the 0 .8 minus and the next two digit value is 0 .03...

Question

Q2 (5 points) If X is a normal random variable with parameters $\mu = 10$ and $\sigma^2 = 36$, compute (a) $P(X > 5)$ (b) $P(4 < X < 16)$ (c) $P(X < 8)$ (d) $P(X < 20)$ (e) $P(X > 16)$

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