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Answer :
Final answer:
In a standard normal distribution, the z value (z^*) that satisfies the condition P(Z < z^*) = 0.025 (or in other words, that leaves a tail probability of 0.025) is -1.96.
Explanation:
The value (z^*) that satisfies the condition (P(Z < z^*) = 0.025), where (Z) is a standard normal random variable can be determined from a standard normal probability table or using a calculator or computer equipped with statistical functions.
The value of z^* that leaves a tail probability of 0.025 is roughly -1.96. We know this by noting that the area to the right of z^* is 0.025 and thus, the area to the left of z^* is 1 - 0.025 = 0.975. Looking this value up in the normal standard probability table, we find that z^* is approximately -1.96. Hence, the correct answer is a) -1.96.
Learn more about Standard Normal Probability here:
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The z-score that corresponds to an area of 0.025 to the left of the z-score in a standard normal distribution is -1.96.
To determine the value z* that satisfies the condition P(Z < z*) = 0.025, where Z is a standard normal random variable, we use the z-score table. Looking up the value that corresponds to an area of 0.025 in the standard normal distribution table, we find that the value that leaves an area of 0.025 to the left is -1.96. This means that 95% of the data lies above -1.96 in a standard normal distribution.
Therefore, the correct answer is -1.96. This is known as the lower tail critical value for a 95% confidence interval or a one-tailed hypothesis test with a significance level of[tex]\(\alpha = 0.05\).[/tex]
