Question

Rudy Researcher is now interested in the drinking habits of students at the University of Alabama. It is known that the average yearly consumptions of soft drinks by college students nationwide is 50 gallons (µ = 50) with a standard deviation of 3.5 gallons (σ = 3.5). Teddy Thirstiman tends to drink a bit more than your average college student. Rudy is very interested in seeing how much Teddy drinks compared to the national average. Teddy drank 59 gallons (X = 59) of soft drinks last year. Probability that can find a student that drinks less than him = P(X<59)=0.9949.

What is the percentile score of Teddy?

Answer 1

Solution,

Given that ,

mean = = 50

standard deviation = = 3.5

P(x < 59 ) = P[(x - ) / < ( 59 - 50 ) / 3.5 ]

= P(z < 2.57)

Using z table

= 0.9949

The percentage is = 99.49%

The percentile is = 99 ^th   percentile

Answer 2

The percentile score of Teddy represents the percentage of students who drank less soft drinks than Teddy. In other words, it indicates where Teddy's consumption of 59 gallons stands relative to the distribution of soft drink consumption among college students nationwide.

To find Teddy's percentile score, we can use the Z-score formula:

Z = (X - µ) / σ

where: X = Teddy's soft drink consumption (59 gallons) µ = Average soft drink consumption of college students nationwide (50 gallons) σ = Standard deviation of soft drink consumption of college students nationwide (3.5 gallons)

Let's calculate Teddy's Z-score:

Z = (59 - 50) / 3.5 Z = 2.57142857143 (rounded to 11 decimal places)

The Z-score tells us how many standard deviations Teddy's consumption is above the national average. A Z-score of 2.57 indicates that Teddy's consumption is 2.57 standard deviations above the average.

Now, we need to find the percentile corresponding to Teddy's Z-score. We can use a standard normal distribution table or a calculator to look up the percentile. From the table or calculator, we find that a Z-score of 2.57 corresponds to a percentile of approximately 99.49%.

Therefore, Teddy's percentile score is approximately 99.49%. This means that Teddy's soft drink consumption of 59 gallons is higher than approximately 99.49% of college students nationwide.