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aleksklad [387]
3 years ago
5

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 2 inches. assume the v

ariable x is normally distributed. left parenthesis a right parenthesis what percent of the fish are longer than 12 ?inches
Mathematics
1 answer:
Kaylis [27]3 years ago
3 0

To solve this problem, we make use of the z statistic. What we have to do here is to find for the z score using the given data and from the standard probability tables for z, we locate the proportion of the fish longer than 12 inches.

 

The formula for calculating the z score is:

z = (x – μ) / σ

where,

x = the sample value = 12 inches

μ = the sample mean = 11 inches

σ = 2 inches

 

so,

z = (12 – 11) / 2

z = 1 / 2

z = 0.5

 

Since we are looking for the values greater than 12, so this is a right tailed test. Using the tables, the value of p at this value of z is:

p (z = 0.5) = 0.3085

 

Therefore there is a 30.85% probability that the fish is longer than 12 inches.

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Answer:

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Step-by-step explanation:

In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;

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The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d

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On substituting, Tn = 4+(n-1)4

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Since the last term is 80, L = 4n

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This shows that the total number of terms in the sequence is 20

According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80 , we are to take the sum of the first 20terms of the sequence. Using summation notation;

4 + 8 + 12 + 16 + 20+ . . . + 80  = \sum ^{20} _{n \to \11} 4n

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