199k views
1 vote
The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm .

a. Find the probability that an individual distance is greater than 204.30 cm.

User Bananafish
by
7.5k points

1 Answer

2 votes

Final answer:

To find the probability that an individual distance is greater than 204.30 cm, calculate the z-score using the formula Z = (X - μ) / σ. Then use the standard normal distribution table to find the corresponding probability.

Step-by-step explanation:

To find the probability that an individual distance is greater than 204.30 cm, we need to calculate the z-score and use the standard normal distribution table. The z-score formula is given by Z = (X - μ) / σ, where X is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get Z = (204.30 - 195) / 8.9 = 1.067. Using the standard normal distribution table, we find that the probability corresponding to a z-score of 1.067 is approximately 0.8577.

Therefore, the probability that an individual distance is greater than 204.30 cm is approximately 0.8577 or 85.77%.

User Bcngr
by
7.1k points