Question

question 36 points 3

given a normal distribution with a mean of 30 and a standard deviation of 5, find the probability of a value which lies between 17 and 25.

0.4953

0.1634

Explanation:

Identify parameters

Using the Normal Distribution Properties knowledge point

$$ \mu = 30, \quad \sigma = 5 $$

Calculate Z-scores

Using the Z-score Calculation knowledge point

$$
LATEXBLOCK0
$$

Find cumulative probabilities

Using the Standard Normal Table knowledge point

$$
LATEXBLOCK1
$$

Calculate interval probability

Using the Interval Probability knowledge point

$$ P(-2.60 < Z < -1.00) = 0.1587 - 0.0047 = 0.1540 $$

Match closest option

Using the Interval Probability knowledge point

$$ 0.1540 \approx 0.1634 \quad (\text{using standard normal table values: } 0.1587 - 0.0047 = 0.1540) $$

Answer:

• (A) 0.4953
• (B) 0.1634 (Correct answer)