Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places.(a) =P>Z1.42(b) =P≤Z1.29(c) =P<−0.63<Z1.96

I'm sorry, but as a text-based AI, I don't have the ability to use an ALEKS calculator. However, I can guide you on how to use the standard normal distribution table to find these probabilities.

(a) P(Z > 1.42) This is the probability that Z is greater than 1.42. To find this, you would look up 1.42 in the Z-table, which gives the probability that Z is less than 1.42. The value you get is 0.9222. But since we want P(Z > 1.42), we need to subtract this from 1 (because the total probability under the curve is 1). So, P(Z > 1.42) = 1 - 0.9222 = 0.0778.

(b) P(Z ≤ 1.29) This is the probability that Z is less than or equal to 1.29. You would look up 1.29 in the Z-table, which gives you 0.9015. So, P(Z ≤ 1.29) = 0.9015.

(c) P(-0.63 < Z < 1.96) This is the probability that Z is between -0.63 and 1.96. To find this, you would find P(Z < 1.96) and P(Z < -0.63), and subtract the two. Looking these up in the Z-table gives you 0.9750 and 0.2624 respectively. So, P(-0.63 < Z < 1.96) = 0.9750 - 0.2624 = 0.7126.

Please note that these are approximate values and might slightly differ based on the exact values in your Z-table.

I'm sorry, but as a text-based AI, I don't have the ability to use an ALEKS calculator. However, I can guide you on how to use the standard normal distribution table to find these probabilities.

(a) P(Z > 1.42) This is the probability that Z is greater than 1.42. To find this, you would look up 1.42 in the Z-table, which gives the probability that Z is less than 1.42. The value you get is 0.9222. But since we want P(Z > 1.42), we need to subtract this from 1 (because the total probability under the curve is 1). So, P(Z > 1.42) = 1 - 0.9222 = 0.0778.

(b) P(Z ≤ 1.29) This is the probability that Z is less than or equal to 1.29. You would look up 1.29 in the Z-table, which gives you 0.9015. So, P(Z ≤ 1.29) = 0.9015.

(c) P(-0.63 < Z < 1.96) This is the probability that Z is between -0.63 and 1.96. To find this, you would find P(Z < 1.96) and P(Z < -0.63), and subtract the two. Looking these up in the Z-table gives you 0.9750 and 0.2624 respectively. So, P(-0.63 < Z < 1.96) = 0.9750 - 0.2624 = 0.7126.

Please note that these are approximate values and might slightly differ based on the exact values in your Z-table.