The scores on a statistics examination are normally distributed with a mean of 5
ID: 3376603 • Letter: T
Question
The scores on a statistics examination are normally distributed with a mean of 55 percent and a standard deviati percent. Calculate the following: 3. a. What percentage of students scored less than 55 percent, -5 % b. What percentage of students scored 90 percent. c. What is the minimum score needed if a student wants to be in the top 5 percent? d. What is the minimum and maximum score that would represent 90 percent of all scores? Exponential Function: Chapter 6 4. You are told that the mean life of a bulb recently manufactured is 2500 hours. Calculate the following: a. A mean life of less than 2500 hours b. Exactly 2500 hours X0 c. More than 2500 hours SBDExplanation / Answer
Ans:
3)
Given that
mean=55
standard deviation=10
a)As,normal distribution is symmetrical about mean,so 50% of the students scores less than 55.
b)z=(90-55)/10=3.5
P(z<3.5)=0.9998 or 99.98%
c)For top 5%:
P(Z>=z)=0.05
P(Z<=z)=1-0.05=0.95
z=1.645
Minimum score=55+1.645*10=71.45
d)cut off for middle 90% is +/-1.645
minimum score=55-1.645*10=38.55
maximum score=55+1.645*10=71.45
4)
Cumulative distribution function:
F(x)=P(X<=x)=1-e-x/2500
a)
P(X<2500)=1-e-(2500/2500)
=1-e-1
=1-0.3679
=0.6321
b)P(X=2500)=(1/2500)*e-(2500/2500)=(1/2500)*e-1=0.00015
c)P(X>2500)=e-(2500/2500)=e-1=0.3679