2. suppose that the durations of high school baseball games are approximately normally distributed with mean 105 minutes and standard deviation 11 minutes.
use a table of standard normal curve areas to find the probability that a randomly selected high school baseball game lasts
a. less than 115 minutes.
b. more than 100 minutes.
c. between 90 and 110 minutes.

a)

With the following code "=NORM.DIST(0.909,0,1,TRUE)"

b)

With the following code "=1-NORM.DIST(-0.455,0,1,TRUE)"

c)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the durationsof high scholl baseball games of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using excel or the normal standard table:

With the following code "=NORM.DIST(0.909,0,1,TRUE)"

Part b

We are interested on this probability

If we apply this formula to our probability we got this:

And we can find this probability using excel or the normal standard table:

With the following code "=1-NORM.DIST(-0.455,0,1,TRUE)"

Part c

If we apply this formula to our probability we got this:

And we can find this probability on this way:

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry