I have the answers, I just need to know how to get them. Please explain, thank y

Question

I have the answers, I just need to know how to get them. Please explain, thank you!

Answers:

a) 81.5%

b) 1.625cm

c) 78.8%

xam 1 Math 163-Fox Name: The width of leaves of the main species of sugar maple is known to be normally distributed with a mean width of 5 cm and a standard deviation of 1.25 cm. For the following problems make sure you show all work. If you are using a calculator, write down the commands. Find the following quantities: 2. What is the probability of a randomly chosen leaf having width between 3.75 cm and 7.5 cm? What width of leaf would be bigger than 65 percent of all leaves? What percentage of leaves have width no less than 4 cm? a. b. c.

Explanation / Answer

mean is 5 and s is 1.25

a) z is (x-mean)/s

P(3.75<x<7.5)=P((3.75-5)/1.25<z<(7.5-5)/1.25)=P(-1<z<2) or P(z<2)-(1-P(z<1)), from normal distribution table we get 0.9772-(1-0.8413)=0.8185 or 81.85%

b) z for 65% from normal table is 0.39 thus answer is mean+z*s=5+0.39*1.25=5.4875 (please re-check the answer, 65% is greater than the mean of 5 and the answer should be more than 5)

c) P(x>4)=P(z>(4-5)/1.25)=P(z>-0.8) or P(z<0.8) =0.7881 or 78.8%

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---