Statistics question

Question

I just need to know where to start for this question. I know it is binomial distribution, but I don't how to calculate the formulas

1.Question 3. A person claims to be able to distinguish between the type of wine with 90% accuracy and presents his claim to an agency interesting in promoting one of the wines. The following experiment is proposed to check his claim:

The man is to taste a wine and indentify it. This is to be done nine times with a three-minute break after each taste. It is agreed that if the man is correct at least six out of the nine times, he will be hired.

a. If the person's claim is true, what is the expected number of correct identifications?
b. If the person's claim is true, what is the likelihood, they will get at least 6 of 9 identifications correct?
c. If the person is just guessing and has a 0.5 probability of correctly identifying the wine, what is the expected number of correct identifications?
d. If the person is just guessing and has a 0.5 probability of correctly identifying the wine, what is the likelihood that they will get at least 6 of 9 correct?
e. If the company wants to decrease the chance of hiring someone who is just guessing to below 15%, how could they modify the test?

Answer 1

90% accuracy

tries nine times

what is expected number of times he's right??

mean== .9^9(9)= . about 3.49

or .9+.9^2

+... .9^9= about 55/9= about 7

= go with 7

or 8 or 9

or

.7x9= .63 = about 6 times

take their average (6+7+8+9+/4= 7.5