Question

Computing Z scores

A teacher wanted to know how well the gifted students in here class perform relative to her other classes. She administers a standardized test with a mean of 50 and standard deviation of 10. Her class of 31 students has an average score of 55, what percent of classes is their average score higher than?


2. A researcher wanted to study the effects of mentoring on intelligence scores. He wanted to know as a baseline what the average intelligence of his students were relative to the general population. He used a standardized IQ test which has a mean of 100 and standard deviation of 16. The 50 students in his study scored an average of 102 on the IQ test. At what percentile of intelligences is the average IQ of his students relative to his population?


3. A rental car company claims the mean time to rent a car on their website is 60 seconds with a standard deviation of 30 seconds. A random sample of 36 customers attempted to rent a car on the website. The mean time to rent was 75 seconds. Is this enough evidence to contradict the company's claim?

Answer 1

a)
u=50
and
0 = 10

n=31

0(T) = 10/31 = 10/5.57 = 1.795

P ( X>55 )=P ( X−μ>55−50 )=P ((X−μ)/σ>(55−50)/1.795)

Since Z=(x−μ)/σ and (55−50)/1.795=2.79 we have:

P ( X>55 )=P ( Z>2.79 )

Use the standard normal table to conclude that:

P (Z>2.79)=0.0026

NOTE: As per the Q&A guidelines I have done the first question please re post the rest Thank you.