32.6k views
0 votes
A population of values has a normal distribution with μ = 163.7 and σ = 45.1. You intend to draw a random sample of size n = 116. Find the probability that a single randomly selected value is between 154.1 and 172.1.

1 Answer

0 votes

Final answer:

To find the probability that a single randomly selected value is between 154.1 and 172.1 in a normal distribution with mean 163.7 and standard deviation 45.1, we can calculate the z-scores for each value and use the standard normal distribution table or calculator to find the probability between these z-scores.

Step-by-step explanation:

To find the probability that a single randomly selected value is between 154.1 and 172.1, we need to calculate the z-scores for these values. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Using the given values of μ = 163.7 and σ = 45.1, we can calculate the z-score for 154.1 as z1 = (154.1 - 163.7) / 45.1 = -0.213 and the z-score for 172.1 as z2 = (172.1 - 163.7) / 45.1 = 0.185.

Next, we use a standard normal distribution table or a calculator to find the area/probability between these z-scores. Subtracting the probability corresponding to the smaller z-score from the probability corresponding to the larger z-score gives us the desired probability.

User Domsom
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories