Multiple Choice 1 point Find the probability that a z-score is between -2.55 and -0.39 . Notice that because it is a $$ z $$-score, we are using the standard normal distribution so mu is 0 and sigma is 1 . 0.3429 0.3483 0.6311 0.6517

Question

UpStudy AI · Accepted Answer

Let the probability be represented as

$$
P(-2.55 \leq Z \leq -0.39) = \Phi(-0.39) - \Phi(-2.55).
$$

Using the symmetry property of the standard normal distribution, we know that

$$
\Phi(-z) = 1 - \Phi(z).
$$

Thus,

$$
\Phi(-0.39) = 1 - \Phi(0.39).
$$

If we look up $$ \Phi(0.39) $$ in the standard normal table, we find approximately

$$
\Phi(0.39) \approx 0.6517.
$$

So,

$$
\Phi(-0.39) \approx 1 - 0.6517 = 0.3483.
$$

Similarly, for $$ z = 2.55 $$,

$$
\Phi(-2.55) = 1 - \Phi(2.55).
$$

Looking up $$ \Phi(2.55) $$, we find approximately

$$
\Phi(2.55) \approx 0.9947.
$$

Thus,

$$
\Phi(-2.55) \approx 1 - 0.9947 = 0.0053.
$$

Now, the probability that $$ Z $$ is between $$-2.55$$ and $$-0.39$$ is

$$
P(-2.55 \leq Z \leq -0.39) \approx 0.3483 - 0.0053 = 0.3430.
$$

Rounding appropriately, we see that the closest option is

$$
\boxed{0.3429}.
$$
The probability that a z-score is between -2.55 and -0.39 is approximately 0.3429.

Multiple Choice 1 point Find the probability that a z-score is between -2.55 and -0.39 . Notice that because it is a \( z \)-score, we are using the standard normal distribution so mu is 0 and sigma is 1 . 0.3429 0.3483 0.6311 0.6517

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Probability Questions