The scores on a statistics examination are normally distributed with a mean of 5

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 SBD

Explanation / 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

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