Given that z is a standard normal random variable, compute the following probabilities.a.&nbsp;P(z≤−1.0)b.&nbsp;P(z≥−1)c.&nbsp;P(z≥−1.5)d.&nbsp;P(−2.5≤z)e.&nbsp;P(−3&lt;z≤0)

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Given that z is a standard normal random variable, compute the following probabilities.a.&amp;nbsp;P(z≤−1.0)b.&amp;nbsp;P(z≥−1)c.&amp;nbsp;P(z≥−1.5)d.&amp;nbsp;P(−2.5≤z)e.&amp;nbsp;P(−3&amp;lt;z≤0)

Unpled · Accepted Answer

Determine the probabilities using table 1 in the appendix (which contains the probabilities to the left of z-scores).  a. P(z≤−1.0)=0.1587  b. P(z≥−1)=1−P(z≤−1)=1−0.1587=0.8413

Louis Smith · Accepted Answer

c. P(z≥−1.5)=1−P(z≤−1.5)=1−0.0668=0.9332    d. P(z≥−2.5)=1−P(z≤−2.5)=1−0.0062=0.9938

Don Sumner · Accepted Answer

e. P(−3&amp;lt;z≤0)=P(z≤0)−P(z≤−3)=0.5000−0.0013=0.4987

fudzisako · Accepted Answer

Step 1:a. P(z≤−1.0)To compute this probability, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives us the probability that a standard normal random variable is less than or equal to a given value.P(z≤−1.0)=Φ(−1.0) where Φ represents the CDF of the standard normal distribution.Step 2:b. P(z≥−1)Similarly, we can use the complement of the CDF to find this probability. The complement of the CDF gives us the probability that a standard normal random variable is greater than a given value.P(z≥−1)=1−Φ(−1)Step 3:c. P(z≥−1.5)Using the same approach as in part (b), we can express this probability as:P(z≥−1.5)=1−Φ(−1.5)Step 4:d. P(−2.5≤z)To compute this probability, we need to find the probability that a standard normal random variable is greater than or equal to a given value.P(−2.5≤z)=1−Φ(−2.5)Step 5:e. P(−3&amp;lt;z≤0)This probability involves finding the difference between two probabilities. We want to find the probability that a standard normal random variable is greater than -3 and less than or equal to 0.P(−3&amp;lt;z≤0)=Φ(0)−Φ(−3) where Φ represents the CDF of the standard normal distribution.By substituting the appropriate values into the equations, you can calculate the numerical values for each of the probabilities.

xleb123 · Accepted Answer

a. To find P(z≤−1.0), we need to calculate the cumulative distribution function (CDF) of the standard normal distribution up to −1.0. Using the standard notation, we can express this probability as P(z≤−1.0)=Φ(−1.0), where Φ(·) represents the CDF of the standard normal distribution.b. Similarly, to find P(z≥−1), we calculate the complement of the CDF up to −1.0. Using notation, we have P(z≥−1.0)=1−Φ(−1.0).c. To find P(z≥−1.5), we compute the complement of the CDF up to −1.5. In notation, this probability is represented as P(z≥−1.5)=1−Φ(−1.5).d. To find P(−2.5≤z), we need to calculate the CDF up to −2.5. Using the notation, this probability can be expressed as P(−2.5≤z)=Φ(−2.5).e. To find P(−3&amp;lt;z≤0), we calculate the difference between the CDF at 0 and the CDF at −3. In notation, this probability is represented as P(−3&amp;lt;z≤0)=Φ(0)−Φ(−3).

Given that z is a standard normal random variable, compute the following probabi

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