Answer :
Final answer:
The probability that a z-score is between 1.57 and 1.84 in a standard normal distribution is 0.025 or 2.5%. This is found by subtracting the probability of 1.57 from the probability of 1.84 using a z-table.
Explanation:
Given a standardized normal distribution, to find the probability that z is between 1.57 and 1.84, we need to refer to a z-table. A z-table tells us the probability up to a certain z-score. Base on the standard normal distribution table or commonly known as Z-table, locate the z-score of 1.84 and 1.57.
We find the probability for z=1.84, and z=1.57, which is 0.9671 and 0.9418 respectively. The area under the curve, which represents the probability, is essentially subtracted from the two figures.
So, to find the probability that a z-score is between 1.57 and 1.84, we need to subtract the two probabilities:
Probability of 1.84 - Probability of 1.57 = 0.9671 - 0.9418
= 0.0253
The answer to the query is 0.025, to the three decimal places. This means there is about a 2.5% chance that a randomly selected value from a normally distributed population will fall between 1.57 and 1.84 standard deviations above the mean.
Learn more about Standard Normal Distribution here:
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