Given that z is a standard normal random variable, compute the following probabilities.P(z ≥ -1.44)Question 2Select one:a.0.7490b.0.9251c.0.0749d.0.5251
Question
Given that z is a standard normal random variable, compute the following probabilities.
P(z ≥ -1.44)
Question 2
Select one:
- a. 0.7490
- b. 0.9251
- c. 0.0749
- d. 0.5251
Solution
To solve this problem, we need to understand that the standard normal distribution has a mean of 0 and a standard deviation of 1. The z-score tells us how many standard deviations away from the mean a value is.
The question asks for the probability that z is greater than or equal to -1.44. In terms of the standard normal distribution, this is the area to the right of -1.44.
We can find this probability using a standard normal distribution table, which gives the probability that a standard normal random variable is less than a given value.
Looking up a z-score of -1.44 in the table, we find a probability of approximately 0.0749. However, this is the probability that z is less than -1.44.
To find the probability that z is greater than or equal to -1.44, we need to subtract the value we found from 1 (because the total probability under the standard normal curve is 1).
So, 1 - 0.0749 = 0.9251.
Therefore, the answer is b. 0.9251.
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