Answer :
a. P(Z < 1.57) is approximately 0.9418.
b. P(Z > 1.84) is approximately 0.0336.
c. P(1.57 < Z < 1.84) is approximately 0.0254.
d. P(Z = 1.57) is approximately zero.
To find the probabilities associated with the standardized normal distribution, we can use a standard normal distribution table or a statistical calculator. Here are the probabilities for the given scenarios:
- a. P(Z < 1.57):
Using a standard normal distribution table or calculator, we find that the probability is approximately 0.9418.
- b. P(Z > 1.84):
Similarly, using a standard normal distribution table or calculator, we find that the probability is approximately 0.0336.
- c. P(1.57 < Z < 1.84):
To find this probability, we need to subtract the probability of Z < 1.57 from the probability of Z < 1.84. Using a standard normal distribution table or calculator, we have:
P(1.57 < Z < 1.84) = P(Z < 1.84) - P(Z < 1.57)
≈ 0.9672 - 0.9418
≈ 0.0254
- d. P(Z = 1.57):
Since the normal distribution is a continuous probability distribution, the probability of Z taking on a specific value is zero.
Please note that the probabilities provided are approximations based on the standard normal distribution.
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