uppose $$ Z $$ follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) $$ P(Z-1.97)=\square $$ (b) $$ P(Z \leq-1.19)=\square $$ (c) $$ P(0.93

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uppose $$ Z $$ follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) $$ P(Z>-1.97)=\square $$ (b) $$ P(Z \leq-1.19)=\square $$ (c) $$ P(0.93

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(a) We have $$ P(Z > -1.97) = 1 - P(Z \le -1.97). $$ Since the standard normal distribution is symmetric, $$ P(Z \le -1.97) = P(Z \ge 1.97) = 1 - P(Z < 1.97). $$ Thus, $$ P(Z > -1.97) = P(Z < 1.97). $$ Using the ALEKS calculator or a standard normal table for $$ z = 1.97 $$, we find $$ P(Z < 1.97) \approx 0.976. $$ --- (b) For $$ P(Z \le -1.19), $$ using the symmetry of the standard normal distribution we have $$ P(Z \le -1.19) = 1 - P(Z < 1.19). $$ Looking up $$ z = 1.19 $$ gives $$ P(Z < 1.19) \approx 0.883. $$ Therefore, $$ P(Z \le -1.19) \approx 1 - 0.883 = 0.117. $$ --- (c) We want to calculate $$ P(0.93 < Z < 2.11) = P(Z < 2.11) - P(Z \le 0.93). $$ From the standard normal table: $$ P(Z < 2.11) \approx 0.983, $$ and $$ P(Z < 0.93) \approx 0.823. $$ Thus, $$ P(0.93 < Z < 2.11) \approx 0.983 - 0.823 = 0.160. $$ --- Answers: (a) $$0.976$$ (b) $$0.117$$ (c) $$0.160$$ (a) 0.976 (b) 0.117 (c) 0.160

uppose follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three
decimal places.
(a)
(b)
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uppose follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) (b) ©