00:01
Hello everyone in this problem we are given that let x denotes the reading speed reading speed of second grade students and here mean is 88 and the standard deviation is given as 12 that x of n of mean is 88 and the standard deviation is 12.
00:49
So here in the first part of the equation we need to find the probability of a randomly selected student in a city will read more than 95 words per minute.
01:04
So here we need to find the probability of x greater than 95.
01:10
So this can be written as probability of x minus mu divided by sigma which is greater than 95 minus 88 where 88 is the mean here and standard deviation is 12.
01:32
So this is nothing but p of z which is greater than simplifying this we have this value to be 0 .58 from the standard variate table we have this value to be 0 .2810.
01:48
So this is the required probability for this part of the equation.
01:52
Now let us move on to the next part of the question.
01:55
So in the next part we need to find the probability that a sample random sample of 12 second grade students from the city results in a mean reading of more than 95 words per minute.
02:13
So it will be we need to find the value of p of x bar which is greater than 95.
02:30
So here this can be written as p of x bar minus mu divided by sigma by square root of n.
02:43
So n we are given with the value as 12.
02:46
So this can be written as this greater than substituting its corresponding values 95 minus 88 divided by 12 divided by square root of 12.
03:04
So this is nothing but z...