Use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial distribution with $n=18$ and $p=0.9$.
Is it appropriate to use a normal distribution to approximate this binomial distribution?
No
Yes
Answer
\(\boxed{\text{No}}\)
Step 1 ：Given a binomial distribution with n = 18 and p = 0.9.
Step 2 ：We need to check if a normal distribution can be used to approximate this binomial distribution.
Step 3 ：The rule of thumb for this approximation is that both np and n(1-p) should be greater than or equal to 5.
Step 4 ：Calculate np and n(1-p):
Step 5 ：np = 18 * 0.9 = 16.2
Step 6 ：n(1-p) = 18 * (1 - 0.9) = 1.8
Step 7 ：Although np is greater than 5, n(1-p) is less than 5.
Step 8 ：Thus, it is not appropriate to use a normal distribution to approximate this binomial distribution.
Step 9 ：\(\boxed{\text{No}}\)
