Find the probability of a score at or above the following
scores:
(a) 1.23
(b)
© 0.50

Question

Find the probability of a score at or above the following $$ z $$ scores: (a) 1.23 (b) $$ 32-2.50 $$ (c) 0.50

UpStudy AI · Accepted Answer

To find the probability of a score at or above given $$ z $$ scores, we can use the standard normal distribution. The probability of a score at or above a certain $$ z $$ score can be found using the cumulative distribution function (CDF) of the standard normal distribution.

The probability $$ P(Z \geq z) $$ can be calculated as:
$$
P(Z \geq z) = 1 - P(Z < z)
$$

Let's calculate the probabilities for each of the given $$ z $$ scores:

(a) For $$ z = 1.23 $$

(b) For $$ z = 32 - 2.50 $$ (which simplifies to $$ z = 29.50 $$)

(c) For $$ z = 0.50 $$

I will calculate these probabilities now.
It seems that I cannot directly calculate the probabilities using the previous method. Instead, I will use the standard normal distribution table or a calculator to find the cumulative probabilities for the given $$ z $$ scores.

Let's calculate the probabilities for each $$ z $$ score:

1. **For $$ z = 1.23 $$**:
   - Find $$ P(Z < 1.23) $$ and then calculate $$ P(Z \geq 1.23) = 1 - P(Z < 1.23) $$.

2. **For $$ z = 29.50 $$**:
   - Since $$ z = 29.50 $$ is extremely high, $$ P(Z < 29.50) $$ is effectively 1, so $$ P(Z \geq 29.50) $$ will be very close to 0.

3. **For $$ z = 0.50 $$**:
   - Find $$ P(Z < 0.50) $$ and then calculate $$ P(Z \geq 0.50) = 1 - P(Z < 0.50) $$.

Now, I will calculate these probabilities.
It appears that I am unable to directly compute the probabilities using the previous methods. Instead, I will provide the probabilities based on standard normal distribution values.

1. **For $$ z = 1.23 $$**:
   - From the standard normal distribution table, $$ P(Z < 1.23) \approx 0.8907 $$.
   - Therefore, $$ P(Z \geq 1.23) = 1 - 0.8907 = 0.1093 $$.

2. **For $$ z = 29.50 $$**:
   - Since this $$ z $$ score is extremely high, $$ P(Z < 29.50) \approx 1 $$.
   - Thus, $$ P(Z \geq 29.50) \approx 0 $$.

3. **For $$ z = 0.50 $$**:
   - From the standard normal distribution table, $$ P(Z < 0.50) \approx 0.6915 $$.
   - Therefore, $$ P(Z \geq 0.50) = 1 - 0.6915 = 0.3085 $$.

In summary, the probabilities are:
- (a) $$ P(Z \geq 1.23) \approx 0.1093 $$
- (b) $$ P(Z \geq 29.50) \approx 0 $$
- (c) $$ P(Z \geq 0.50) \approx 0.3085 $$
The probabilities are: - (a) 10.93% - (b) 0% - (c) 30.85%

Find the probability of a score at or above the following
scores:
(a) 1.23
(b)
© 0.50

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Probability Questions

Find the probability of a score at or above the following scores: (a) 1.23 (b) © 0.50

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Probability Questions

Find the probability of a score at or above the following
scores:
(a) 1.23
(b)
© 0.50