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Chapter 4: Q. 91 (page 269)

Seed weight (2.2) Biological measurements of the same species often follow a normal distribution quite closely. The mean weights of seeds of a variety of winged beans are approximately normal, with a mean of 525milligrams (mg) and a standard deviation of 110mg.

a. What percent of seeds weigh more than 500mg?

b. If we discard the lightest 10%of these seeds, what is the smallest weight among the remaining seeds?

Short Answer

Expert verified

a. The percentage of seeds weighing more than 500gms isP(X>500)=0.5899.

b. The smallest weight of the seed, after discarding the lightest 10%,is Lightest weight = 384.20gm

Step by step solution

01

Part (a) STEP 1: Given information

We need to find the percentage of seeds whose weight is more than 500mg.

02

Part (a) STEP 2: Explanation

X=The same species' biological measurements

is N(525,110)

For X=500,

width="182" height="21" role="math">(500-525)/110=-0.23

ThusP(X>500)=P(z>-0.23)=1-P(z<-0.23)

P(X>500)=1-0.4101=0.5899gms

03

Part (b) STEP 1: Given information

We have been given that the mean weights of seeds of a variety of winged beans are approximately normal, with a mean of milligrams (mg) and a standard deviation of 110mg.

04

Part (b) STEP 2: Explanation

The lightest weights are those which are underneath z=-1.28

localid="1654058832720" 525-1.28脳110

Corresponding Xscore =384.20gms

The littlest weight among the remaining seeds is 384.20gms.

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