Answer:
a) 
With:


b) 

c) 

d) 


Step-by-step explanation:
For this case we know the following propoertis for the random variable X

We select a sample size of n = 81
Part a
Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

With:


Part b
We want this probability:

We can use the z score formula given by:

And if we find the z score for 89 we got:


Part c

We can use the z score formula given by:

And if we find the z score for 75.65 we got:


Part d
We want this probability:

We find the z scores:



The 2 triangles in the big triangle are similar so we can write
3x / 3x - 2 = 5x / 3x
9x^2 = 15x^2 - 10x
6x^2 - 10x = 0
x(6x - 10) = 0
x= 0 or 5/3
Answer:
3/4 is less < than 5/6
Step-by-step explanation:
From the plot, the masses of the five smallest sodium chloride samples are all 1/4 ounce. Therefore, we can calculate for their total mass by multiplying the mass by 5:
total mass = 1/4 ounce * 5
= 5/4 or 1.25 ounces
We can get the same result even if we compute for the total mass by taking the sum of their masses:
total mass = 1/4 + 1/4 + 1/4 + 1/4 + 1/4
= 5/4 oz.