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# Statistics home work help

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Must show all your work step by step in order to receive the full credit; Excel is not allowed. (26-37)

Solve the following problems using the binomial tables:
If n=50 and p=.40, find P(x=11)
If n=100 and p=.20, find P(x>10)
If n=20 and p= .60, find P(x<13)
If n=20 and p=.80, find P(x≤ 14)
If n=20 and p=.30, find P(5≤X≤8)
If n=20 and p=.70, find P(X≥15)

Ten trials are conducted in a Bernouli process in which the probability of success in a given trial is 0.6. If x= the number of successes, determine the following:
E(x)
σx

P(x=5)
P(4≤x≤8)
P(3≤x≤7)

The proportion of consumers favoring a new product is p = 0.80 A sample of n = 10 persons is randomly selected. Use the binomial formula to determine the probabilities for the following number of consumer favoring a product.
Exactly 5 d. Greater then 2

Greater than or equal to 3 e. Less than 4

Less than or equal to 9 f. Equal to 7

Suppose 20% of the people in the city prefer Pepsi cola as their soft drink. If a random sample of 6 is chosen, the number of Pepsi drinkers could vary from 0 to 6. Shown here are the numbers of Pepsi drinkers occurring in the sample. Use the data to determine the mean number or pepsi drinkers in a sample of 6 in the city and compute the standard deviation.

Pepsi drinkers probability
0 .373
1 .247
2 .019
3 .211
4 .002
5 .118
6 .030

Find a Z score, call it Zo, such that:
P (Z < Zo) = 0.9808
P (Z < Zo) = 0.9850
P (-Zo ≤Z ≤Zo) = 0.95
P (-Zo ≤Z ≤Zo) = 0.9
P (-Zo ≤Z ≤Zo) = 0.6826
P (-Zo ≤ Z ≤Zo) = 0.9950

Let the random variable x be normally distributed with mean 5 and variance 4, Find the following probabilities.
P(X≥ 5.7)
P(X≤ 3.4)
P(5.7 ≤ X ≤ 5.8)

Using the normal probabilities table, calculate the areas under the standard normal curve for the following z values

Between Z=0.0 and Z= 1.2
Between Z=0.0 and Z= -0.9
Between Z= -1.71 and Z= -2.03
Between Z= -1.72 and Z= 2.53
Greater than Z= 2.50
Greater than Z= -0.60
Less than Z= -1.22
Less than Z= 1.66

Find x_0 from the following probabilities given that μ=160,σ=16.

a. P(X>x_0 )=0.8770

b. P(X< x_0 )=0.12

c. P(X<x_0 )=0.97

d. P(〖136 ≤X ≤x〗_0 )=0.4808

e. P(x_(0 )≤X ≤204)=0.8185

f. P(180≤〖X≤x〗_0 )=0.0919

Find the Z scores for the following normal distribution problems.

a. µ = 604, σ = 56.8, P(X ≤ 635)

b. µ = 48, σ2 = 144, P(X < 20)

c. µ = 111, σ = 33.8, P(100 ≤ X ≤ 150)

d. µ = 264, σ2 = 118.81, P(250 < X < 255)

e. µ = 37, σ = 4.35, P(X > 35)

f. µ = 156, σ = 11.4, P(X ≥ 170)

Find the value of x if the random variable X is normally distribution with mean 50 and variance 36.

a. P(X ≥ x) = 0.0655

b. P(X ≤ x) = 0.8686

c. P(40 ≤ X ≤ x) = 0.6715

d. P(x ≤ X ≤ 50) = 0.3531

Find the following probabilities:

a. P(-1.4 < Z < 0.6)

b. P(Z > -1.44)

c. P(Z < 2.03)

d. P(Z > 1.67)

e. P(Z < 2.84)

f. P(1.14 < Z < 2.43)

Suppose that the following data are randomly selected from a population of normally distributed values:

4 5 6 5 5

Find a 80% confidence interval from the mean μ.

Find a 95% confidence interval from the mean μ.

Find a 98% confidence interval from the mean μ.

https://brainmass.com/statistics/solving-binomial-problems-560647

#### Solution Preview

Hi there,

Thanks for letting me work on your post. I've included my explanations in the word document.

Must show all your work step by step in order to receive the full credit; Excel is not allowed. (26-37)

Solve the following problems using the binomial tables:
If n=50 and p=.40, find P(x=11)=0.0057
If n=100 and p=.20, find P(x>10)=1-0.0023=0.9977
If n=20 and p= .60, find P(x<13)=0.5841
If n=20 and p=.80, find P(x≤ 14)=0.1958
If n=20 and p=.30, find P(5≤X≤8)=P(x<=8)-P(x<=4)=0.8867-0.2375=0.6492
If n=20 and p=.70, find P(X≥15)=1-P(x<=14)=1-0.5836=0.4164.

Ten trials are conducted in a Bernouli process in which the probability of success in a given trial is 0.6. If x= the number of successes, determine the following:
E(x)=10*0.6=6
σx= sqrt(10*0.6*0.4)=1.5492

P(x=5)=0.2007
P(4≤x≤8)=P(x<=8)-P(x<=3)=0.9536-0.0548=0.8988
P(3≤x≤7)=P(x<=8)-P(x<=2)=0.9536-0.01223=0.9413

The proportion of consumers favoring a new product is p = 0.80 A sample of n = 10 persons is randomly selected. Use the binomial formula to determine the probabilities for the following number of consumer favoring a product.
Exactly 5
P(x=5)=10C5*0.8^5*(1-0.8)^(10-5)=0.0264
d. Greater then 2

P(x>2)=1-P(x=0)-P(x=1)-P(x=2)=1-10C0*0.8^0*(1-0.8)^10-10C1*0.8*(1-0.8)^9-10C2*0.8^2*(1-0.8)^8=0.999922

Greater than or equal to 3
P(x>=3)=P(x>2)=0.999922
Less than 4

P(x<4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)=10C0*0.8^0*0.2^10+10C1*0.8*0.2^9+10C2*0.8^2*0.2^8+10C3*0.8^3*0.2^7=0.0008644

Less than or equal to 9
P(x<=9)=1-P(x=10)=1-10C10*0.8^10*0.2^0=0.8926
f. Equal to 7
P(x=7)=10C7*0.8^7*0.2^3=0.2013

Suppose 20% of the people in the city prefer Pepsi cola as their soft drink. If a random sample of 6 is chosen, the number of Pepsi drinkers could vary from 0 to 6. Shown here are the numbers of Pepsi drinkers occurring in the sample. Use the data to determine the mean number or pepsi drinkers in a sample of 6 in the city and compute the standard deviation.

Pepsi drinkers probability
0 .373
1 .247
2 ...

#### Solution Summary

The expert solves binomial problems to compute standard deviation.

\$2.19