Company wants to hire no more then 140 workers. There are 450 people taking test. Probability of passing test is 0.3

[Ryuuzaki]

Company wants to hire no more then [MATH]140[/MATH] workers. Competence test is being held, there are [MATH]450 [/MATH]people taking it. Probability of passing test is [MATH]0.3[/MATH], whats the probability that company will have problems with excess candidaties?


X-Number of people that passed the test is random variable with binomial distribution. Parameters [MATH]n=450, p=0.3[/MATH]
[MATH]P(X>140)=1-P(X\leq 140)[/MATH]

What should be my next step in this exercise?
There's a hint from my profesor on website but I am not sure how to use it:
"find value of standard normal distribution from tables"

 

[Deleted member 4993]

Company wants to hire no more then [MATH]140[/MATH] workers. Competence test is being held, there are [MATH]450 [/MATH]people taking it. Probability of passing test is [MATH]0.3[/MATH], whats the probability that company will have problems with excess candidaties?


X-Number of people that passed the test is random variable with binomial distribution. Parameters [MATH]n=450, p=0.3[/MATH]
[MATH]P(X>140)=1-P(X\leq 140)[/MATH]

What should be my next step in this exercise?
There's a hint from my profesor on website but I am not sure how to use it:
"find value of standard normal distribution from tables"

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[HallsofIvy]

The binomial distribution B(n, p, q) (with p+ q= 1) has mean np and standard deviation \(\displaystyle \sqrt{npq}\). For large n that can be approximated by the normal distribution with that mean and standard distribution. For this problem the mean is \(\displaystyle \mu= 450(0.3)= 135\) and standard deviation \(\displaystyle \sigma= \sqrt{450(0.3)(0.7)}= \sqrt{94.5}= 9.72\) approximately.

 

[Ryuuzaki]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

X-Number of people that passed the test is random variable with binomial distribution. Parameters [MATH]n=450, p=0.3[/MATH]
[MATH]P(X>140)=1-P(X\leq 140)[/MATH]
Normal distribution

[MATH]N(135;9,72(1))[/MATH]
[MATH]X\leq 140 = P(U\leq0.51)=\Phi(0.51)=0.69065[/MATH]
[MATH]\Phi[/MATH] is distribution of [MATH]N(0;1)[/MATH] so [MATH](PX>140)=1-0.6965=0.3035[/MATH]

 

[Dr.Peterson]

There's a hint from my professor on website but I am not sure how to use it:
"find value of standard normal distribution from tables"

What have you been taught about the normal approximation to the binomial distribution?

 

[Ryuuzaki]

What have you been taught about the normal approximation to the binomial distribution?

Nothing, I have to do my own research since the only thing I am getting from profesor during the pandemic is tasks to solve without any help from him .
What I wrote in my previous post is based on some other examples I found on internet

 

[Dr.Peterson]

So you have no textbook or class notes to use? That's risky, as different people each a topic like this in different ways, so that mix-and-match learning can be very confusing. Have you found anything about the continuity correction, or about rules to decide whether the normal approximation is appropriate?

 

[Ryuuzaki]

So you have no textbook or class notes to use? That's risky, as different people each a topic like this in different ways, so that mix-and-match learning can be very confusing. Have you found anything about the continuity correction, or about rules to decide whether the normal approximation is appropriate?

Yeah gathering all those things from different websites/videos is very confusing.

About continuity correction I found this video to be most helpful:

If I am right this could be literally translated into my task:
16=140
30=450
0.4=0.3

So I did just that
[MATH]np=450 \times 0.3 = 135 > 5[/MATH][MATH]nq=450 \times 0.7 = 315 >5[/MATH][MATH]npq = 450 \times 0.3 \times 0.7 = 94.5[/MATH][MATH]X \sim N (135.94.5)[/MATH] approx

[MATH]P(X<140) \rightarrow (Px<135.5)[/MATH]
[MATH]P= (\phi<\frac{135.5-135}{\sqrt{94.5}})[/MATH][MATH]P= (\phi<0.0514)[/MATH]And for the last part in 8:50 timestamp, guy in video speaks about value depending on tables that I got. What should I use here?

 

[Dr.Peterson]

How did you get P(X<140)→(Px<135.5) ? And why are you using P(X<140) rather than P(X≤140) as before?

Other than these details, you are doing well.

As for the tables, he's probably referring to the fact that some tables may have more precision than others. The one I checked had two decimal places for z (like most I've seen), so I looked up 1.30 and got 0.9032. A calculator or computer could take a more precise input.

 

[Ryuuzaki]

Thanks for help, I submitted this answer and 2 previous tasks to moodle.
Hopefully profesor will be satisfied since I can't correct anything anymore.