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Answer :
Since this is the standard distribution, you can look up the value for z<1.57 in the standard normal distribution table.
This represents the area under curve shaded grey in below picture.
The area is 0.94179. (So, it's not a calculation, but a lookup).
This represents the area under curve shaded grey in below picture.
The area is 0.94179. (So, it's not a calculation, but a lookup).
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Final answer:
The probability that a random variable from a standardized normal distribution is less than 1.57 is approximately 0.9418. For a z-score of 1.27, the equivalent probability is about 0.8980.
Explanation:
The standardized normal distribution is a statistical distribution where the mean is 0 and the standard deviation is 1. To compute the probability of a value being less than a certain z-score, such as 1.57, we can utilize z-tables or statistical software.
The value listed in the z-table for a score of 1.57 is approximately 0.9418, which represents the probability that the random variable is less than 1.57.
In the context of a measurement error, if we want to calculate the probability that a single sample from a standard normal distribution (e.g., measurement error or e) is less than 1.27, we would refer to the z-table or software to find that the probability P[e < 1.27] is about 0.8980.
