Answer:
a)
And we can find this probability like this:
b)
And using the z score we got:
c)
And if we use the continuity correction we got:
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".
Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.
Part a
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Part a
For this case we want to find this probability:
And if we use the z score given by:
We got this:
And we can find this probability like this:
Part b
For this case we want this probability:
And if we use the continuity correction we got:
And using the z score we got:
Part c
For this case we want this probability:
And if we use the continuity correction we got: