Question

initial knowledge check question 18 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) $p(z \leq -0.82) = \square$ (b) $p(z > 0.62) = \square$ (c) $p(-0.50 < z < 2.06) = \square$

Explanation:

Step1: Find $P(Z \leq -0.82)$

Use standard normal table/calculator.
$P(Z \leq -0.82) = 0.2061$

Step2: Calculate $P(Z > 0.62)$

Use complement rule: $P(Z > 0.62) = 1 - P(Z \leq 0.62)$
$1 - 0.7324 = 0.2676$

Step3: Calculate $P(-0.50 < Z < 2.06)$

Use $P(Z < 2.06) - P(Z \leq -0.50)$
$0.9803 - 0.3085 = 0.6718$

Answer:

(a) $0.206$
(b) $0.268$
(c) $0.672$