population size=50
population mean= 80m
standard deviation = 0.70m
what proportion would have average meter of 89 or more?
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now I know how to solve this problem if the question is worded "what proportion would have average meter Greater than 89?" but since this question ask for the proportion that is greater than and inclusive of 89 I am not sure if I should still workout and look up z value in the normal distribution (u=0, sigma=1)table.Maybe I should use a different table? or a different formula?
Help please!
To calculate the proportion of individuals with an average meter of 89 or more, you can use the standard normal distribution and the z-score formula.
First, let's calculate the z-score for an average meter of 89 using the formula:
z = (x - μ) / σ
where:
x = 89 (average meter)
μ = 80m (population mean)
σ = 0.70m (standard deviation)
z = (89 - 80) / 0.70
z = 9 / 0.70
z ≈ 12.86
Now, since the question asks for the proportion that is greater than or equal to 89, you need to calculate the area under the normal curve to the right of the z-score.
You can use a standard normal distribution table or a statistical calculator to find the area to the right of 12.86.
Using a standard normal distribution table, you would find the area to the left of 12.86 (since tables usually provide the cumulative probability to the left of a particular z-value) and then subtract it from 1 to get the area to the right.
However, it's worth noting that most standard normal distribution tables only provide values up to a certain number of decimal places. Since the z-value in this case is quite large, it might not be available in standard tables.
In such cases, you can use statistical software or online calculators specifically designed to calculate proportions for extreme values. These tools use sophisticated algorithms to compute the probabilities accurately.
Alternatively, you can use the z-table values available to you and make an approximation for the proportion by rounding the z-value to the nearest value in the table and using the corresponding area.
Remember that due to rounding, this approximation may not be exact but can give us an estimate.
I recommend using an online statistical calculator or software to find the accurate proportion or use a z-table with a high level of precision.