Question

STATISTICS QUESTION- HIGHER LEVEL

If you randomly select 30 students multiple times, and ask for their scores on quiz two what is the probability that the mean score for the 30 students is higher than Molly's score on quiz two? Please show and explain your work.

Molly scored an 89.
The mean score for quiz two was 84, and the standard deviation was 5.

Answer 1

To find the probability that the mean score for the 30 students is higher than Molly's score on quiz two, calculate the z-score for Molly's score and find the probability using the standard normal distribution. Therefore, the probability that the mean score for the 30 students is higher than Molly's score on quiz two is approximately 0.1587, or 15.87%.

Step-by-step explanation:

To find the probability that the mean score for the 30 students is higher than Molly's score on quiz two, we need to find the z-score for Molly's score and then find the probability of obtaining a higher mean score using the standard normal distribution.

Step 1: Calculate the z-score for Molly's score:

Z = (X - μ) / σ

Z = (89 - 84) / 5 = 1

Step 2: Calculate the probability of obtaining a higher mean score:

Using a standard normal distribution table or a calculator, we can find that the probability of obtaining a z-score greater than 1 is approximately 0.1587.

Therefore, the probability that the mean score for the 30 students is higher than Molly's score on quiz two is approximately 0.1587, or 15.87%.