00:01
Hello students in this question given mu equals to 60 sigma is 9 and n equals to 25 so x bar follows normal distribution with 60 comma 9 by root 25 that is a.
00:18
Next for b probability of x bar less than 60 and this can be written as probability of x bar minus mu divided by sigma by root n is less than 60.
00:31
Minus mu that is 60 divided by 9 by root 25 that is probability of z less than 0 and that is this is 0 less than this and that is equal to 0 .5 and for the next question that is c probability of x less than a equal to 0 .3 so probability of x minus mu divided by sigma by root n is less than a minus mu divided by sigma by root n and that is equal to 0 .3 so from the table this is probability of z less than z equals to 0 .3 so from the table z equal to minus 0 .5 to 4.
01:26
So that is a minus mu divided by sigma by root n equals to minus 0 .5 to 4.
01:34
So the value of a is 59 .06.
01:46
And for the next question, probability of x bar lies between 56 and 62.
01:57
This can be written as probability of 56 minus 60 divided by 9 by root 25 less than x bar minus mu divided by sigma by root n, that is z minus 62 minus 60 divided by 9 by root 25.
02:16
And this is equal to probability of z lies between minus 2 .22 and 1 .11.
02:25
That is probability of z less than 1 .11 minus probability of z less than minus 2 .22.
02:34
And here the answer is 0 .8536...