Question 7
Learning Check 4
Find the probability of a score at or above the following
z scores:
(a) 1.23
(b)
© 0.50
(

Question

Question 7 Learning Check 4 Find the probability of a score at or above the following z scores: (a) 1.23 (b) $$ 72-2.50 $$ (c) 0.50 (

UpStudy AI · Accepted Answer

(a) For $$ z = 1.23 $$, we need to find  
$$
P(Z \ge 1.23) = 1 - \Phi(1.23),
$$  
where $$\Phi(z)$$ is the cumulative distribution function (CDF) of the standard normal distribution. Looking up $$\Phi(1.23)$$ (or using a calculator), we find  
$$
\Phi(1.23) \approx 0.8907.
$$  
Thus,  
$$
P(Z \ge 1.23) \approx 1 - 0.8907 = 0.1093.
$$

(b) For $$ z = -2.50 $$, we calculate  
$$
P(Z \ge -2.50) = 1 - \Phi(-2.50).
$$  
Using the symmetry of the normal distribution, we know  
$$
\Phi(-2.50) = 1 - \Phi(2.50).
$$  
Looking up $$\Phi(2.50)$$ gives approximately  
$$
\Phi(2.50) \approx 0.9938.
$$  
Then,  
$$
\Phi(-2.50) \approx 1 - 0.9938 = 0.0062,
$$  
so  
$$
P(Z \ge -2.50) \approx 1 - 0.0062 = 0.9938.
$$

(c) For $$ z = 0.50 $$, we have  
$$
P(Z \ge 0.50) = 1 - \Phi(0.50).
$$  
Checking the table,  
$$
\Phi(0.50) \approx 0.6915.
$$  
Thus,  
$$
P(Z \ge 0.50) \approx 1 - 0.6915 = 0.3085.
$$
(a) The probability of a score at or above $$ z = 1.23 $$ is approximately 0.1093. (b) The probability of a score at or above $$ z = -2.50 $$ is approximately 0.9938. (c) The probability of a score at or above $$ z = 0.50 $$ is approximately 0.3085.

Question 7
Learning Check 4
Find the probability of a score at or above the following
z scores:
(a) 1.23
(b)
© 0.50
(

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Question 7 Learning Check 4 Find the probability of a score at or above the following z scores: (a) 1.23 (b) © 0.50 (

Upstudy AI Solution

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Beyond the Answer

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Question 7
Learning Check 4
Find the probability of a score at or above the following
z scores:
(a) 1.23
(b)
© 0.50
(