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Answer :
The probability P(114172) is approximately 0.1587, or 15.87%.
The probability of an event can be calculated by using the z-score formula and the standard normal distribution table. The z-score represents the number of standard deviations a data point is from the mean.
To find the probability P(114172), we need to convert it to a z-score.
The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x is the data point,
μ is the mean, and
σ is the standard deviation.
In this case, we have:
x = 114,
μ = 143, and
σ = 29.
Plugging these values into the formula, we get:
z = (114 - 143) / 29
Calculating this, we find that the z-score is approximately -0.999.
Now, we can use the standard normal distribution table or a calculator to find the probability associated with this z-score. The table or calculator will give us the probability of a z-score being less than -0.999.
Assuming a standard normal distribution, we can use a table to find that the probability P(z < -0.999) is approximately 0.1587.
Therefore, the probability P(114172) is approximately 0.1587, or 15.87%.
To learn more about probability here:
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