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Westkost [7]
3 years ago
8

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. based on a large number of obser

vations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. what is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
7 0
The normal distribution curve for the problem is shown below

We need to standardise the value X=405.5 by using the formula

z-score= \frac{X-Mean}{Standard Deviation}
z-score= \frac{405.5-402.7}{8.8} =0.32

We now need to find the probability of z=0.32 by reading the z-table

Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:

P(Z\ \textgreater \ z)=1 - P(Z\ \textless \ z)

from  the z-table, the reading P(Z\ \textless \ 0.32) gives 0.6255

hence, 
P(Z\ \textgreater \ 0.32)=1-0.6255=0.3475

The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%

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