5.2.4
Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using technology.
A.) P(x=1)
B.) P(x=5)
C.) P(x=3)
D.) P(x 3)
E.) P(x5)
F.) P(x4)
X ~ binomial (n,p)
Where n = 6 , p = 0.30
Binomial probability distribution is
P(X) = nCx px (1-p)n-x
A)
P (X = 1) = 6C1 0.301 0.705
= 0.3025
b)
P (X = 5) = 6C5 0.305 0.701
= 0.0102
c)
P (X = 3) = 6C3 0.303 0.703
= 0.1852
d)
P( X <= 3) = 1 - P (X >= 4)
= 1 - [ P (X = 4) + P (X = 5) + P( X = 6) ]
= 1 - [ 6C4 0.304 0.702 +6C5 0.305 0.70 +6C6 0.306 0.700 ]
= 1 - 0.0705
= 0.9295
e)
P (X >= 5) = P( X = 5) + P (X = 6)
= 6C5 0.305 0.70 +6C6 0.306 0.700
= 0.0109
f)
P (X <= 4) = 1 - P( X >= 5)
= 1 - 0.0109
= 0.9891
5.2.4 Suppose a random variable, x, arises from a binomial experiment. If n = 6, and...
(3 points): Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities (it is acceptable to use some form of technology such as web applet, Excel, calculator, etc.). a.) P(x = 1) b.) P(x = 5) c.) P(x = 3) d.) P(x ≤ 3) e.) P(x ≥ 5) f.) P(x≤4)
Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the following probabilities using the binomial formula. a.) P( x = 5) b.) P( x = 8) c.) P( x = 12) d.) P( x ≤ 4) e.) P( x ≥ 8) f.) P( x ≤12)
show calculator command for 2 please 2. Suppose a random variable, x, arises from a binomial experiment. If n = 22, and p = 0.85, find the following probabilities using the binomial formula. Show calculator command used. a. (2 pts) P(x = 18) = b. (2 pts) P(x 3) = c. (2 pts) P(x220) = 3. The proportion of red M&M's in a milk chocolate packet is approximately 21% (Madison, 2013). Suppose a package of M&M's typically contains 52 M&M's....
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upposes is a binomial random variable with n = 5 and , 2,3,4, and , using the foll. Compute p(x) for x 0, 1, 2, 3, 4, and 5, using a. List th S for Success and F for Failure on each trial) corresponding to each value of x, assign probabilities to each sample point, and obtain p= wing two methods e sample points (take p(x) by adding sample-point probabilities tion to obtain p(x) b. Use the formula for the...
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f(31–43 10.320.72 543 Computing Binomial Probabilities If X is a binomial random variable with parameters n and p, the probability distribution of Xis given by f(k) = P(X=k) = (pkan* for k =0, 1. , .,where q=1-p. Example: Suppose n = 5 and p = 0.3. Then q = 1 - p = 0.7, f(k)= 10.3)* (0.75% f(0)=C6 20.3)%0.7)-1-1-(0.16807)-0.16807. f(1)=( )(0,3)(0.7) 10.3)(0.2401) - 5(0.07203)0.36015 0 0.1681 f(2)=(3 10.3)2(0.73 (0.09)(0.343) – 10(0.03087)-0.30870 1 0.3602 0.027)(0.49) =10(0.01323)-0.132302 0.3087 f(4)=( )(0.3)*(0.7) (0.0081)(0.7) -5(0.00567)=0.0284...
2. Let X be a binomial variable with n=10. Suppose E(X) - 3. (a) (5 points) What is the probability of success of the binomial experiment that generates the variable X? Explain your answer. (b) (5 points) Find P(X = 3). (c) (5 points) Find P(3 < X < 7). (d) (5 points) Find P(X 1 )
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 3), n = 9, p = 0.3 Probability = (b) P(X > 4), n = 5, p = 0.3 Probability = (c) P(X<5), n = 7.p = 0.35 Probability = (d) P(X > 6), n = 7, p = 0.3 Probability =
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