Answer:
89% of pebbles weigh more than 2.1 grams.
Step-by-step explanation:
Given that
Mean = 2.6
SD = 0.4
As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first
[tex]z = \frac{x-mean}{SD}\\z = \frac{2.1-2.6}{0.4}\\z = -1.25[/tex]
Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1
So,
[tex]P(x<-1.25) = 0.10565[/tex]
This gives us the probability of P(z<-1.25) or P(x<2.1)
To find the probability of pebbles weighing more than 2.1
[tex]P(x>2.1) = 1 - P(x<2.1) = 1 - 0.10565 = 0.89435[/tex]
Converting into percentage
[tex]0.89435*100 = 89.435\%[/tex]
Rounding off to nearest percent
89%
Hence,
89% of pebbles weigh more than 2.1 grams.
