Question

How much do you study? A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 29 and standard deviation 7.Use T1-B4 calculator to find following.

(a) Find the 92nd percentile of tho number of hours studying.
(b) Find the 37 percentile of the number of hours studying.

Answer 1

The question pertains to finding the 92nd and 37th percentiles in a normal distribution using the given mean and standard deviation. This involves identifying the Z-score for each percentile and then calculating the corresponding value using the mean and standard deviation.

Step-by-step explanation:

The question involves finding the percentiles in a normal distribution which is a common task in statistics, a branch of mathematics. Since the distribution of the study hours is normally distributed, we can use the Z-score table or a calculator with statistical functions to find the specific percentiles.

Finding the 92nd Percentile

For the 92nd percentile, we want the value below which 92% of the data falls. Given the mean (μ) is 29 hours and the standard deviation (σ) is 7 hours:

1. Find the Z-score that corresponds to the 92nd percentile.
2. Use the formula X = μ + Zσ, where X is the number of study hours.

Finding the 37th Percentile

For the 37th percentile, follow a similar process as for the 92nd percentile but find the Z-score that corresponds to 37% instead.

Without the actual functions of a T1-B4 calculator being specified, we have to assume it includes functions to calculate percentiles from a normal distribution. If you were using such a function, you would insert the mean, standard deviation, and the desired percentile to get the corresponding number of hours studied.