0:00
Hello student.
00:01
So in this problem, 10 dice are rolled, which means n is equal to 10.
00:05
And here we have to find the sum of the values obtained is between 30 and 40 inclusive.
00:12
So for that, the rolling of dice, they have uniform probability obtaining any number from 1 to 6, which means, so x has the uniform probability from 1 to 6.
00:35
So the mean of the dice rolled is 6 plus 1 divided by 2, which is equal to 3 .5.
00:46
So here it is n is equal to 10, 10 times we are rolling the dice.
00:51
So mu is equal to n into 3 .5, which is equal to 30.
01:00
Then the standard deviation sigma squared is equal to mu squared minus 1 divided by 12, which is equal to 35 divided by 12.
01:19
And here the standard deviation, that is variance, variance is equal to sigma is equal to n into 35 divided by 12, which is equal to 350 divided by 12.
01:39
Now the probability of getting the sum of the values between 30 and 40 inclusive can be written as p of 30 lesser than or equal to x, which is lesser than or equal to 40...