00:01
Hello students, according to the given question we have to find out the probability values given mu is equal to 183, sigma is equal to 30.
00:10
X will follows normal distribution with mu comma sigma square.
00:15
In the b bit to find probability that x greater than 190 that is equal to probability of x minus mu by sigma greater than 190 minus 183 by 30.
00:27
So, that is equal to probability of z greater than 0 .2334.
00:33
From z table it is 0 .4077 that is 40 .77 percent.
00:40
In the c bit probability of 140 less than x less than 160 that is equal to probability of 140 minus 183 by 30 less than z less than 160 minus 183 by 30.
00:56
So, which is equal to probability of minus 1 .4334 less than z less than minus 0 .7667.
01:06
From z table it is 0 .1458 approximately 14 .58 percent.
01:15
Now, in the d bit we have to find the inter quartile range.
01:18
So, here the middle 50 percent of values lies between the probability of minus z less than z less than z is equal to 50 percent.
01:30
So, from z table z is equal to minus 0 .674 and z is equal to 0 .674...