Question

Fill in the blanks. Optionshouse tracked the performance of their most active day traders and found that the probability of a winning call option pick was 0.5375. If in a day, 458 call options are picked by these traders, around __________ of them will be winners, give or take __________. Assume each pick is independent.a. 246.2, 113.8500 b. 246.2, 10.67 c. 10.67, 246.2 458, d. 10.67 246.2, 0.5375

Answer 1

Answer:

If in a day, 458 call options are picked by these traders, around   246.2  of them will be winners, give or take  10.67  .

Step-by-step explanation:

Hello!

Your study variable is X: the number of winning calls in a sample of 458 calls.

The variable has a binomial distribution since you have two possible outcomes, that the call is a winning call (success) or that the call is not a winning call (failure), each call is independent and the probability of success is p= 0.5375 and the probability of failure q= 1-p= 1-0.5375= 0.4625.

The expected value for a binomial distribution is

E(X)= n*p= 458 * 0.5375= 246.175

And to know the standard error (or standard deviation) you have to calculate the square root of the variance:

V(X)= n*p*q= 458*0.5375*0.4625= 113.85

√V(X)= √113.85= 10.67

I hope it helps!