Question

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 $525$milligrams (mg) and a standard deviation of $110$mg.

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

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

Short answer

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

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

Step-by-step solution

Part (a) STEP 1: Given information

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

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

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

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

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 $110$mg.

Part (b) STEP 2: Explanation

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

localid="1654058832720" $525-1.28\times 110$

Corresponding $X$score $=$$384.20$gms

The littlest weight among the remaining seeds is $384.20$gms.