Let X be a binomial random variable with p = 0.7 and n = 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to four decimal places (e. g. 98.7654).

0.4114  

0.0006  

0.1091  

0.1957  

Step-by-step explanation:

Given:  

p = 0.7 n = 10

We need to determine the probabilities using table , which contains the CUMULATIVE probabilities P(X x).  

a. The probability is given in the row with n = 10 (subsection x = 3) and in the column with p = 0.7 of table:  

P(X  3) = 0.4114  

b. Complement rule:  

P( not A) = 1 - P(A)

Determine the probability given in the row with n = 10 (subsection x = 10) and in the column with p = 0.7 of table:  

P(X  10) = 0.9994

Use the complement rule to determine the probability:  

P(X > 10) = 1 - P(X 10) = 1 - 0.9994 = 0.0006  

c. Determine the probability given in the row with n = 10 (subsection x = 5 and x = 6) and in the column with p = 0.7 of table:  

P(X  5) = 0.8042

P(X  6) = 0.9133

The probability at X = 6 is then the difference of the cumulative probabilities:  

P(X = 6) = P(X  6) - P(X  5) = 0.9133 — 0.8042 = 0.1091  

d. Determine the probability given in the row with n = 10 (subsection x = 5 and x = 11) and in the column with p = 0.7 of table:  

P(X  5) = 0.8042

P(X  11) = 0.9999

The probability at 6 X 11 is then the difference between the corresponding cumulative probabilities:  

P(6  X 11) = P(X 11) - P(X  5) = 0.9999 — 0.8042 = 0.1957  

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!