Question

A distribution has a mean of 40 and a standard deviation of 5 . Which of the below best represents the percentile rank for a score of 50 ? 15% 30% 95% 50% Question 4 (1 point) Given a critical z of +1.65 and an observed z of +1.20, you should reject the null hypothesis fail to reject the null hypothesis postpone any decision conduct another test, using a larger sample size

Answer 1

To determine the percentile rank for a score of 50 in a distribution with a mean of 40 and a standard deviation of 5, we can calculate the z-score for the score of 50 and then use a standard normal distribution table to find the corresponding percentile rank.

The z-score formula is:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

Plugging in the values:

z = (50 - 40) / 5

z = 10 / 5

z = 2

To find the percentile rank corresponding to a z-score of 2, we can consult a standard normal distribution table or use a calculator. A z-score of 2 corresponds to a percentile rank of approximately 97.7%.

Therefore, none of the provided options (15%, 30%, 95%, 50%) best represents the percentile rank for a score of 50. The correct answer is not given in the options.

Regarding the second part of your question, given a critical z-score of +1.65 and an observed z-score of +1.20, you would fail to reject the null hypothesis. This is because the observed z-score (+1.20) is smaller than the critical z-score (+1.65).