What is the area under the standard normal curve that lies between Z = -0.76 and

Question

What is the area under the standard normal curve that lies between Z = -0.76 and Z = 1.13? a. 3708 b. 6472 c. 2764 d. 3528 Serum cholesterol levels were taken from a population of college students. The results were normally distributed Males had a mean of 195 and a standard deviation of 10. Females had a mean of and a standard a 12. According to the Empirical Rule, what percent of males have a cholesterol level above 215? a. 5% b. 2.5% c. 95% d. 25% The time between infection with the AIDS virus and developing AIDS has been estimated as a normal distribution with an average time of 8 years and a standard deviation of 2 years. According to the Empirical Rule. what percent of the time does it take less than 4 tears after infection to develop AIDS? A. 16% b. 1% c. 2.5% d. 32% e. 5%

Explanation / Answer

Part One:

Area between -0.76 & 1.13

= 0.8708 – 0.2236

= 0.6472

Part Two:

According to empirical rule, 95% of the data lies between two standard deviations (2*10=20) on either side of the mean(195), i.e. in the range 175-215.

So P(M>215) ~ 5/2 = 2.5%

(Optional Detailed calculation follows):

Since =195 and =10 we have:

P ( X>215 )=P ( X>215195 )=P ( (X)/>(215195)/10)

Since Z=(x)/ and (215195)/10=2 we have:

P ( X>215 )=P ( Z>2 )

Step 3: Use the standard normal table to conclude that:

P (Z>2)=0.0228

Part three:

According to empirical rule, 95% of the data lies between two standard deviations (2*2=4) on either side of the mean(8), i.e. in the range of 4-12.

So P(T<4) ~ 5/2 = 2.5%

Kindly Upvote if Helpful :)

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.