00:01
Hi guys, in this problem, for part, let x1 up to x25 denote the weights of adobe products in the sample.
00:12
So each xi, we have xi, okay, for i equals 1, 2, 3, up to 25.
00:26
Okay, so it's a normal random variable with mu, equal, equals 3 pounds and a standard deviation of 0 .25.
00:37
So no, we know that x -dash equals 1 over 25 times x1 plus x2 up to x25.
00:51
Okay, so okay.
00:56
Now this representing the mean weight of the sample and it's also a random very was the mean new equals 0 point mean equals 3 and the standard deviation so let's compute the standard deviation okay so the similar deviation over the square root of 25 equals 0 .05 okay so now let's use the table of cameality standard normal distribution to find the full ability of x dash less than 2 .95 so it's the probability of z where d less than negative 1 okay so this is 0 .1587 okay now in part p we need to find the value of x such that probability of x -mere than x equals 0 .99 by standardizing this probability expression can puritan as the probability of z more than x minus 3 over 0 .05 okay so this is 1 minus probability of z less than or equal x minus 3 over 0 .05 okay so this is 0 .99.
02:38
Now let's see equal x minus 3 over 0 .05.
02:48
Then we need to find the table in the table of the community standard normal distribution such as the value of z, such as probability of z less than or equal z equals 0 .01...