00:02
Hello students, according to the given question we have to find the probability values.
00:06
Given mu is equal to 500, sigma is equal to 100.
00:11
So to find probability that x less than 750 is equal to probability of x minus mu by sigma is less than 750 minus 500 is divided by 100.
00:25
So that will be equal to probability of z is less than 2 .5.
00:31
From z table it is 0 .9938 approximately 99 .38%.
00:39
Now for the b bit to find the 90th percentile.
00:45
So that can be written as probability of x less than x is equal to less than or equal to x is equal to 90%.
00:54
So probability of x minus mu by sigma less than or equal to x minus 500 divided by 100 is equal to 0 .90.
01:07
From z table, from the z table probability of z less than or equal to 1 .282 is equal to 0 .90.
01:22
Now by comparing both equations we get x minus 500 divided by 100 is equal to 1 .282.
01:32
Then x is equal to 1 .282 into 100 plus 500.
01:39
So that is equal to 628 .2...