Probability of an event is the measure of its chance of occurrence. The event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

<h3>How to get the z scores?</h3>

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

$X \sim N(\mu, \sigma)$

(X is following normal distribution with mean $\mu$ and standard deviation $\sigma$ )

then it can be converted to standard normal distribution as

$Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)$

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

$P(Z \leq z) = P(Z < z) )$

Also, know that if we look for Z = z in z tables, the p-value we get is

$P(Z \leq z) = \rm p \: value$

Using the z-table, we get the needed probabilities as:

Case 1:

$P(-1.25 \leq Z \leq 0.25) = P(Z \leq 0.25) - P(Z \leq -1.25) \approx 0.5987 - 0.1056 = 0.4931$

Case 2:

$P(-1.25 \leq Z \leq 0.75) = P(Z \leq 0.75) - P(Z \leq -1.25) \approx 0.7734- 0.1056=0.6678$

Case 3:

$P(0.25 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.25) \approx 0.8944 - 0.5987=0.2957$

Case 4:

$P(0.75 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.75) \approx 0.8944 - 0.7734 =0.1210$

Thus, the event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

Learn more about z-scores here:

brainly.com/question/13299273

5 0

2 years ago

The table shows the rental charges for two car rental companies. For each, there is a flat rental fee, plus a charge per mile dr

sattari [20]

This was probably not answered on time
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3 years ago