Consider the following. (Give your answers correct to four decimal places.)
(a) Find P(-2.07 < z < 0.00).
(b) Find P(-1.86 < z < 2.11).
(c) Find P(z < -1.55).
(d) Find P(z < -0.55).
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http://davidmlane.com/hyperstat/z_table.html
Thank you
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To answer these questions, we need to refer to the standard normal distribution table, also known as the z-table. The z-table provides the area under the standard normal curve to the left of a given z-value.
(a) To find P(-2.07 < z < 0.00), we need to find the area to the left of 0.00 and subtract the area to the left of -2.07.
- The area to the left of 0.00 is 0.5000 (as 0.00 is the mean of the standard normal distribution).
- The area to the left of -2.07 is 0.0192 (from the z-table).
Therefore, P(-2.07 < z < 0.00) = 0.5000 - 0.0192 = 0.4808.
(b) To find P(-1.86 < z < 2.11), we need to find the area to the left of 2.11 and subtract the area to the left of -1.86.
- The area to the left of 2.11 is 0.9821 (from the z-table).
- The area to the left of -1.86 is 0.0314 (from the z-table).
Therefore, P(-1.86 < z < 2.11) = 0.9821 - 0.0314 = 0.9507.
(c) To find P(z < -1.55), we need to find the area to the left of -1.55.
The area to the left of -1.55 is 0.0606 (from the z-table).
Therefore, P(z < -1.55) = 0.0606.
(d) To find P(z < -0.55), we need to find the area to the left of -0.55.
The area to the left of -0.55 is 0.2912 (from the z-table).
Therefore, P(z < -0.55) = 0.2912.
Remember to always refer to the z-table for accurate values of the standard normal distribution.