Answer :
The probability that z is between 1.57 and 1.87 is approximately 0.0275. This would also give us a result of approximately 0.0275.
Assuming you are referring to the standard normal distribution, we can use a standard normal table or a calculator to find the probability that z is between 1.57 and 1.87.
Using a standard normal table, we can find the area under the curve between z = 1.57 and z = 1.87 by subtracting the area to the left of z = 1.57 from the area to the left of z = 1.87. From the table, we can find that the area to the left of z = 1.57 is 0.9418, and the area to the left of z = 1.87 is 0.9693. Therefore, the area between z = 1.57 and z = 1.87 is:
0.9693 - 0.9418 = 0.0275
So the probability that z is between 1.57 and 1.87 is approximately 0.0275.
Alternatively, we could use a calculator to find the probability directly using the standard normal cumulative distribution function (CDF). Using a calculator, we would input:
P(1.57 ≤ z ≤ 1.87) = normalcdf(1.57, 1.87, 0, 1)
where 0 is the mean and 1 is the standard deviation of the standard normal distribution. This would also give us a result of approximately 0.0275.
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