Answer:
a)
And we can find this probability with the complement rule:
b)
And if we use the z score we got:
Step-by-step explanation:
Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:
Where and
Part a
We are interested on this probability
And we can use the z score formula given by:
And using this formula we got:
And we can find this probability with the complement rule:
Part b
For this case we select a sample of n =44 and the new z score formula is given by:
And if we find the z score we got:
And if we use the z score we got: