Answer :
Answer:
The standard deviation of weight for this species of cockroaches is 4.62.
Step-by-step explanation:
Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
To find : What is the approximate standard deviation of weight for this species of cockroaches?
Solution :
We have given,
Mean [tex]\mu=50[/tex]
The sample mean x=55
A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
i.e. P(X>55)=14%=0.14
The total probability needs to sum up to 1,
[tex]P(X\leq 55)=1-P(X>55)[/tex]
[tex]P(X\leq 55)=1-0.14[/tex]
[tex]P(X\leq 55)=0.86[/tex]
The z-score value of 0.86 using z-score table is z=1.08.
Applying z-score formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where, [tex]\sigma[/tex] is standard deviation
Substitute the values,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]1.08=\frac{55-50}{\sigma}[/tex]
[tex]1.08=\frac{5}{\sigma}[/tex]
[tex]\sigma=\frac{5}{1.08}[/tex]
[tex]\sigma=4.62[/tex]
The standard deviation of weight for this species of cockroaches is 4.62.
Answer:
a 4.6 on the text BTW
Step-by-step explanation:
bye good luck