MHB -aux04 Species of insect is normally distributed

AI Thread Summary
The lifespan of a specific insect species follows a normal distribution with a mean of 57 hours and a standard deviation of 4.4 hours. Standardization of the lifespan values yielded z-scores of -0.45 for 55 hours and 0.68 for 60 hours. The probability of an insect living more than 55 hours is approximately 67%, while the probability of living between 55 and 60 hours is around 43%. Further calculations using rational numbers provided similar results for these probabilities. A follow-up question regarding the lifespan of 90% of the insects will be addressed in future discussions.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
just seeing how I did on this one:confused:

The lifespan of a particular species of insect is normally distributed with a mean of $57$ hours and a standard deviation of $4.4$ hours.

this is the normal distribution with $\mu = 57$ and $\sigma = 4.4$

View attachment 1026
tried to standardize this by $\frac{55-75}{4.4}=-0.45$ and $\frac{60-57}{4.4}=0.68$

with $\mu = 0$ and $\sigma = 1$ and $P(-0.45 < x < 0.68)$
which hopefully looks like the given graph on the right belowhttps://www.physicsforums.com/attachments/1027View attachment 1028

(a) What are the values of $a$ and $b$
from the standard $\frac{x-\mu}{\sigma} a=-0.45$ and $b=0.68$

(b) Find the probability that the lifespan of an insect of this species is more than $55$ hours

$P(55 < X)$ from $z$ score $0.45$ then $0.1736 + .5 = .6736$ or $\approx 67\%$

View attachment 1029

(b) Find the probability that the lifespan of an insect of this species is between $55$ and $60$ hours

$0.2517+0.1736=0.4253$ or $\approx 43\%$
 
Last edited:
Mathematics news on Phys.org
Re: species of insect is normally distributed

Using rational numbers instead of decimal approximations:

a) $$a=-\frac{5}{11},\,b=\frac{15}{22}$$

Using numeric integration for comparison:

b) $$P(55<X)\approx0.675282$$

c) $$P(55<X<60)\approx0.427605$$

I would say you did them correctly.
 
Re: species of insect is normally distributed

well that is encouraging. there still is one more question on this but I will post it tomorrow. :)
 
90% of the insects die after t hours.

(i) Represent this information on a standard normal curve diagram indicating clearly the area representing $90\%$.

(ii) Find the value of $t$.does this mean $P(X < t)$, also should $60 < t$ I don't see where this $90\%$ is supposed to be since P(55 < X < 60) was [FONT=MathJax_Main]0.427605
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top