00:01
Hello students, according to the given question we have to find the probability values.
00:06
So, it was given mean mu is equal to 74 .0, sigma is equal to 3 .2.
00:14
In the a bit to find probability that x is less than 70 that will be equal to probability of x minus mu by sigma is less than 70 minus 74 by 3 .2.
00:27
So, that is equal to probability of z less than minus 1 .25.
00:33
So, from z table it is 0 .1056 approximately 10 .56 percent.
00:40
In the b bit probability of x greater than or equal to x is equal to 10 percent.
00:46
So, then probability of x minus mu by sigma is greater than or equal to x minus 74 by 3 .2 is equal to 0 .10.
00:58
From z table from the z table x minus 74 by 3 .2 is equal to 1 .282 from z table.
01:09
Then x is equal to 1 .282 into 3 .2 plus 74, then x value is equal to 78 .10.
01:22
Now, in the c bit probability of x is less than 70 is equal to 2 percent that means 0 .02.
01:31
From z table z value is minus 2 .05, it is from z table at this probability.
01:38
So, z is equal to x minus mu by sigma that implies minus 2 .05 is equal to 70 minus 74 by sigma is unknown.
01:50
Then sigma is equal to 70 minus 74 by minus 2 .05.
01:56
So, which is equal to 1 .95...