Further Maths Standard Deviation Question (Need Urgent Help)

[12Many]

In a large population of moths, the number of eggs per cluster is approximately normally distributed with a mean of 165 eggs and a standard deviation of 25 eggs.

Using the 68-95-99.7% rule determine
i. The percentage of clusters expected to contain more than 140 eggs
ii. the number of clusters expected to have less than 215 eggs in a sample of 1000 clusters

c. The standardized number of eggs in one cluster is given by z= -2.4
Determine the actual number of eggs in this cluster

[Lear]

Hi what part are you stuck on? If you could show some working out we could help you learn by fixing errors instead of giving you the answer

[12Many]

Hi what part are you stuck on? If you could show some working out we could help you learn by fixing errors instead of giving you the answer

I'm stuck on those 3 questions. I have no idea where to start

[michaeljacksonftw]

In a large population of moths, the number of eggs per cluster is approximately normally distributed with a mean of 165 eggs and a standard deviation of 25 eggs.

Using the 68-95-99.7% rule determine
i. The percentage of clusters expected to contain more than 140 eggs
ii. the number of clusters expected to have less than 215 eggs in a sample of 1000 clusters

c. The standardized number of eggs in one cluster is given by z= -2.4
Determine the actual number of eggs in this cluster

hi 
i. 140 = 165-25 = mean - standard deviation, mean - standard deviation is 16%, so more than 140 eggs is 84%, in other words (100%-16%)
ii. 215 = 165 + 2(25) = mean + 2*standard deviation = 2.5%, so 2.5% of 1000 = 25
so 1000-25 = 975
c. standard score = (actual score - mean)/(standard deviation)
-2.4 = (actual score - 165)/(25)
(actual score - 165)/(25) = -2.4
(actual score - 165) = -60
actual score = -60+165
actual score = 105

Hope these answers help 

[12Many]

hi 
i. 140 = 165-25 = mean - standard deviation, mean - standard deviation is 16%, so more than 140 eggs is 84%, in other words (100%-16%)
ii. 215 = 165 + 2(25) = mean + 2*standard deviation = 2.5%, so 2.5% of 1000 = 25
so 1000-25 = 975
c. standard score = (actual score - mean)/(standard deviation)
-2.4 = (actual score - 165)/(25)
(actual score - 165)/(25) = -2.4
(actual score - 165) = -60
actual score = -60+165
actual score = 105

Hope these answers help 

Thank you for the help ( bonus points for formulating your answer)