I only need help with e and f please. The mean yearly rainfall in Sydney, Austra

Question

I only need help with e and f please.

The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm ("Annual maximums of," 2013). Assume rainfall is normally distributed. a.) State the random variable. b.) Find the probability that the yearly rainfall is less than 100 mm. c.) Find the probability that the yearly rainfall is more than 240 mm. d.) Find the probability that the yearly rainfall is between 140 and 250 mm. e.) If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or why not? What rainfall amount are 90% of all yearly rainfalls more than? f)

Explanation / Answer

Sol:

P(X<100)

pnorm(100,mean=137,sd=69)

=0.2958992

z score for 100

z=100-137/69

=-37/69

=-0.5362319

its unsusual

as it is 0.5362319 standard deviations below mean

Solutionf:

Z score for 90 th percentile is

qnorm(0.9)=1.281552

1.281552=x-mean/sd

1.281552=x-137/69

x=1.281552*69+137

x=225.4271

rainfall amount 90% of all yearly rainfall more than 225.4271

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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