13% of people took a math course. What is the probability that in a 350 randomly selected sample, less than 40 people take the course?

Jadon Melendez 2022-07-22 Answered
13 % of people took a math course. What is the probability that in a 350 randomly selected sample, less than 40 people take the course?

So I have X B i n ( 350 , 13 100 )
Then let Y N ( 13 100 , 0.00032314 2 )
I want P ( X < 40 ) = P ( p ^ < 4 10 )
Then P ( z < 4 10 13 100 0.00032314 2 ) which is obviously very wrong.
Where did it go wrong, and why did it go wrong?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Octavio Barr
Answered 2022-07-23 Author has 11 answers
The number X of people taking the course is B ( n , p )-distributed with n = 350 , p = 0.13. Its variance is npq, n p q , q := 1 p. The z-score of X is Z := X n p n p q , so the Normal approximation of P ( X < 40 ) is
P ( Z < 40 n p n p q ) = P ( Z < 40 350 × 0.13 350 × 0.13 × 0.87 ) .
(Depending on how you seek to discretize the Normal variable approximating X, you might replace 40 with e.g. 39.5.)
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-05-07
Suppose
where x is normal with mean μ and variance σ. Then I see how to derive mode of f ( y ) (distribution of y), as we need to find the value y that makes
f ( y ) == 0
However, why is mode not simply
e μ ?
y is a monotonic function of x, and so when x reaches its mode, then y should also reach its mode. The mode of x is its mean ( μ) hence y's mode should be
e μ
what mistake have I made?
asked 2022-07-14
What are the two types of hypotheses used in a hypothesis test? How are they related?
asked 2022-06-30
The operation is of two step.
1. Bin a data in 10 bins. (the distribution is unimodal) and
2. Then find the bin with maximum density.
In other words finding the mode of a distribution.
asked 2022-07-19
What is the z-score of X, if n = 25, μ = 60 , SD = 12, and X =58?
asked 2022-07-18
The measure of effect size used with the X 2 test of independence is
a.That there is a small effect size
b. That there is a medium effect size
c. That there is a large effect size
d. That there is no effect size at all
asked 2022-06-21
need to generate some random data from lognormal distribution, where I set the mode and standart deviation of that lognormal distribution. For this purpose I choose to use random numbers generator from lognormal distribution. This generator takes two numbers, that are mean and sd of underlying normal distribution.
So far its clear I need to derive mean and sd of normal distribution, which is underlaying for lognormal distribution where I know mode and sd. I know the equations for derivation of mean and sd:
NOTATION:
n ( x ) = mean of normal distribution
s d ( x ) = s d of normal distribution
n ( y ) = mean of lognormal distribution
s d ( y ) = sd of lognormal distribution
m o d e ( y ) = mode of lognormal distribution
EQUATIONS:
n ( x ) = 2 l n ( n ( y ) ) ( 1 / 2 ) l n ( s d ( y ) 2 + n ( y ) 2 )
s d ( x ) = 2 l n ( n ( y ) ) + l n ( s d ( y ) 2 + n ( y ) 2 )
m o d e ( y ) = e x p ( n ( y ) s d ( y ) 2 )
Here I stuck because I cant get the equation for n ( y ) from these equations, that I need to compute n ( x ). So far I ended:
m o d e ( y ) = e x p ( 4 l n ( n ( y ) ) 3 / 2 l n ( n ( y ) 2 s d ( y ) 2 ) )
m o d e ( y ) 2 / 3 s d ( y ) 2 = n ( y ) 2 ( n ( y ) 2 / 3 m o d e ( y ) 2 / 3 )
Can anybody help me to complete this derivation?
asked 2022-07-20
What is the z-score of sample X, if n = 121 , μ = 23 , S t . D e v . = 110 , a n d   E X = 43

New questions

The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The pro?t contributions are $200 per unit for model DRB and $280 per unit for model DRW. The linear programming model for this problem is as follows:
Max 200DRB + 280DRW
s.t.
20DRB + 25DRW 40,000 Steel Available
40DRB + 100DRW ? 120,000 Manufacturing minutes
60DRB + 40DRW ? 96,000 Assembly minutes
DRB, DRW ? 0
Optimal Objective Value = 424000.00000
Variable Value blackuced Cost
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
DRB 1000.00000 0.00000
DRW 800.00000 0.00000
Constraint Slack/ Surplus Dual Value
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1 0.00000 8.80000
2 0.00000 0.60000
3 4000.00000 0.00000
Objective Allowable Allowable
Variable Coef?cient Increase Decrease
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
DRB 200.00000 24.00000 88.00000
DRW 280.00000 220.00000 30.00000
RHS Allowable Allowable
Constraint Value Increase Decrease
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1 40000.00000 909.09091 10000.00000
2 120000.00000 40000.00000 5714.28571
3 96000.00000 Infnite 4000.00000
a. What are the optimal solution and the total profit contribution?
b. Another supplier offeblack to provide Deegan Industries with an additional 500 pounds of the steel alloy at $2 per pound. Should Deegan purchase the additional pounds of the steel alloy? Explain.
c. Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain.
d. Because of increased competition, Deegan is considering blackucing the price of model DRB such that the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain.
e. If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain.