Question

decide whether you can use the normal distribution to approximate the binomial distribution. if you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. if you cannot, explain why and use the binomial distribution to find the indicated probabilities. a survey of adults found that 7% say their favorite sport is auto racing. you randomly select 600 adults and ask them to name their favorite sport. complete parts (a) through (d). determine whether a normal distribution can be used to approximate the binomial distribution. choose the correct answer below. a. no, because nq < 5. b. no, because np < 5. c. yes, because both np ≥ 5 and nq ≥ 5.

Explanation:

Step1: Identify values of n, p and q

Let \(n = 600\) (sample - size), \(p=0.07\) (probability of success), then \(q = 1 - p=1 - 0.07 = 0.93\).

Step2: Calculate np and nq

Calculate \(np\): \(np=600\times0.07 = 42\). Calculate \(nq\): \(nq=600\times0.93 = 558\).

Step3: Check the normal - approximation condition

The condition for approximating a binomial distribution with a normal distribution is \(np\geq5\) and \(nq\geq5\). Since \(np = 42\geq5\) and \(nq = 558\geq5\), the normal distribution can be used.

Answer:

C. Yes, because both \(np\geq5\) and \(nq\geq5\)