what is the probability by Pr( X ≥ 8) years where X is normally distributed with mean 5.24 and sd = 1.90?
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We estimate the probability by Pr( X ≥ 8) years where X is normally distributed with mean 5.24 and sd = 1.90.
Assuming normal distribution we want prob that x >=8
P(x>=8) = P(Z >= (8 - 5.24)/1.90) = P(Z >= 1.45) = 1 - P(Z<1.45) =
use a z-score table to find the portion of the population below 1.45 sd above the mean
looks like about .93
so prob X ≥ 8 is ... 1 - .93
To find the probability that X is greater than or equal to 8, where X is a normally distributed random variable with a mean of 5.24 and a standard deviation of 1.90, we can use a standard normal distribution table or a statistical software.
However, in this case, we can use the properties of the standard normal distribution to transform our random variable X into a standard normal variable Z. This is done by calculating the z-score.
The z-score (also known as the standard score) measures how many standard deviations an observation or data point is from the mean of the distribution. It is calculated as:
z = (X - μ) / σ
Where X is the value of the random variable, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability Pr(X ≥ 8). To do this, we first calculate the z-score of 8 using the formula above:
z = (8 - 5.24) / 1.90
z = 1.442
Once we have the z-score, we can then use it to find the probability using a standard normal distribution table or a statistical software.
Using a standard normal distribution table, we can look up the probability associated with a z-score of 1.442. The table provides the area to the left of the z-score. Since we want the probability that X is greater than or equal to 8, we need to find the area to the right of the z-score (1 - the area to the left).
Alternatively, we can also use statistical software or built-in functions in spreadsheets or programming languages to find the probability directly. These functions usually take in the z-score as the argument and provide the probability or percentile associated with that z-score.