Question

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).

Answer 1

Answer:

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 $\leq$ 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 $\leq$  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 $\leq$  10) = 0.9994

Use the complement rule to determine the probability:  

P(X > 10) = 1 - P(X$\leq$ 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 $\leq$  5) = 0.8042

P(X $\leq$  6) = 0.9133

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

P(X = 6) = P(X $\leq$  6) - P(X $\leq$  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 $\leq$  5) = 0.8042

P(X $\leq$  11) = 0.9999

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

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