3. (a) Helen Comrie, a scientist, is studying the ozone and forest density in Fr

Question

3. (a) Helen Comrie, a scientist, is studying the ozone and forest density in France. She has observed that ozone level X in US is approximately normally distributed with mean about 65.9 ppb and standard deviation of 23.3 ppb. Find i. the probability that the ozone level in US is greater than 80. ii. the probability that the ozone level in US between 40 and 90. 3 marks] 3 marks] (b) Suppose that the calculus GPA at a university, Y, is normally distributed with mean 2.2 and 95% of the time, the GPA is between 1.6 and 2.8. Find the standard deviation 4 marks of Y

Explanation / Answer

3a)(i) P(X>80)=1-P(X<80)=1-P(Z<(80-65.9)/23.3)=1-P(Z<0.6052)=1-0.7275 =0.2725

(ii) P(40<X<90)=P((40-65.9)/23.3<Z<(90-65.9)/23.3)=P(-1.1116<Z<1.0343)=0.8495-0.1332=0.7164

b)

for 95% CI ; criical z =1.96

hence std deviation =(2.8-2.2)/1.96=0.3061

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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