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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: 12Many on May 17, 2018, 08:47:08 pm

Title: Further Maths Standard Deviation Question (Need Urgent Help)
Post by: 12Many on May 17, 2018, 08:47:08 pm

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

Title: Re: Further Maths Standard Deviation Question (Need Urgent Help)
Post by: Lear on May 17, 2018, 08:59:35 pm

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 :)

Title: Re: Further Maths Standard Deviation Question (Need Urgent Help)
Post by: 12Many on May 17, 2018, 10:00:45 pm

Quote from: Lear on May 17, 2018, 08:59:35 pm

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

Title: Re: Further Maths Standard Deviation Question (Need Urgent Help)
Post by: michaeljacksonftw on May 17, 2018, 10:10:36 pm

Quote from: 12Many on May 17, 2018, 08:47:08 pm

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  ;D

Title: Re: Further Maths Standard Deviation Question (Need Urgent Help)
Post by: 12Many on May 17, 2018, 11:01:55 pm

Quote from: michaeljacksonftw on May 17, 2018, 10:10:36 pm

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  ;D

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