Question

In: Math

Assume that x is a binomial random variable with n = 100 and p = 0.40....

Assume that x is a binomial random variable with n = 100 and p = 0.40. Use a normal
approximation (BINOMIAL APPROACH) to find the following: **please show all work**
c. P(x ≥ 38) d. P(x = 45) e. P(x > 45) f. P(x < 45)

Expert Solution

Solution :

Given that,

p = 0.40

q = 1 - p =1-0.40=0.60

n = 100

Using binomial distribution,

= n * p = 100*0.40=40

= n * p * q = 100*0.40*0.60=4.8990

Using continuity correction ,

(C)P(x ≥ 38 ) = 1 - P(x <37.5)

= 1 - P((x - ) / < (37.5 - 40) /4.8990 )

= 1 - P(z <-0.51 )

= 1 - 0.3050

=0.6950

(d)Using continuity correction ,

P(x = 45)= P[(44.5 - 40)/4.8990 ) < (x - ) / < (45.5 - 40) /4.8990 ]

= P( 0.92< z < 1.12)

= P(z <1.12 ) - P(z <0.92 )

=0.8686 - 0.8212

=0.0474

(E)P(x >45 ) = 1 - P(x <45)

= 1 - P((x - ) / < (45.5 - 40) /4.8990 )

= 1 - P(z <1.12 )

= 1 - 0.8686

=0.1314

(F)P(x <45 )= P((x - ) / < (44.5 - 40) /4.8990 )

= P(z <0.92 )

=0.8212

milcah answered 6 months ago

Assume that x is a binominal random variable with n=100 and p=0.40. Use a normal approximation...

Assume that x is a binominal random variable with n=100 and p=0.40. Use a normal approximation to find the following: a) P(x≥38) b) P(x=45) c) P(x>45) d) P(x<45)

X is a binomial random variable. n= 100 p= .4 Use the binomial approach and normal...

X is a binomial random variable. n= 100 p= .4 Use the binomial approach and normal approximation to calculate the follwowing: 1. P(x>=38) 2. P(x=45) 3. P(X>45) 4. P(x <45)

Given a binomial random variable with n = 100 and p = .5, estimate the Pr[X...

Given a binomial random variable with n = 100 and p = .5, estimate the Pr[X ≥ 40]

Suppose that x is a binomial random variable with n = 5, p = .66, and...

Suppose that x is a binomial random variable with n = 5, p = .66, and q = .34. (b) For each value of x, calculate p(x). (Round final answers to 4 decimal places.) p(0) = p(1)= p(2)= p(3)= p(4)= p(5) (c) Find P(x = 3). (Round final answer to 4 decimal places.) (d) Find P(x ≤ 3). (Do not round intermediate calculations. Round final answer to 4 decimal places.) (e) Find P(x < 3). (Do not round intermediate calculations....

X1 is a binomial random variable with n = 100 and p = 0.8, while X2...

X1 is a binomial random variable with n = 100 and p = 0.8, while X2 is a binomial random variable with n = 100 and p = 0.2. The variables are independent. The profit measure is given by P = X1 / X2. Run N = 10 simulations of X1 and X2 to simulate the distribution of P, and then find both the variance and the semi-variance.

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x)...

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x) = n x p x (1 − p) n−x x = 0, 1, 2, ..., n 0 Otherwise Show that a) Pn x=0 f(x) = 1 [10 Marks] b) the MGF of X is given by [(1 − p) + pet ] n . Hence or otherwise show that E[X]=np and var(X)=np(1-p).

Let x be a binomial random variable with n=7 and p=0.7. Find the following. P(X =...

Let x be a binomial random variable with n=7 and p=0.7. Find the following. P(X = 4) P(X < 5) P(X ≥ 4)

Suppose x is a binomial random variable with p = .4 and n = 25. c....

Suppose x is a binomial random variable with p = .4 and n = 25. c. Use the binomial probabilities table or statistical software to find the exact value of P(x>=9). Answ:.726 back of book d. Use the normal approximation to find P(x>=9). answ:.7291 the back of book For one I have no idea how to use the binomial probabilities table . The mean is 10, variance is 6 and std is 2.45 If possible could someone explain how to...

Let X be a binomial random variable with parameters n = 5 and p = 0.6....

Let X be a binomial random variable with parameters n = 5 and p = 0.6. a) What is P(X ≥ 1)? b) What is the mean of X? c) What is the standard deviation of X? (Show work)

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a...

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a binomial random variable with parameters (m, p). What is the pdf of the random variable Z=X+Y? (b) Let X and Y be indpenednet random variables. Let Z=X+Y. What is the moment generating function for Z in terms of those for X and Y? Confirm your answer to the previous problem (a) via moment generating functions.