True of False? Please answer as many as you can, and show work please! thank you

Question

True of False? Please answer as many as you can, and show work please! thank you in advance.

1) Suppose the random variable X represents the side of the car where your gas cap is located {left side, right side}and the probability of a gas cap being located on the right side is 0.5. The location of gas caps is known to follow a binomial distribution, if you look at 6 cars, then 3 is the most likely outcome for gas caps located on the left side of the car.
2) Suppose the rate of return for on a proposed investment can be best
described by a normal distribution with mean 10% and standard deviation
3%. Then probability that the rate of return for the investment equals
exactly 10% is 0.5
3) In a linear regression, when performing a hypothesis test on the slope
(?1), the null hypothesis (Ho) is always that the slope (?1) is equal to zero
and the alternative hypothesis (H1) is always that there is a positive linear
relationship between the input variable X and the output variable Y

Explanation / Answer

1) Given is a binomial distribution B(n,p) with n =6, p=0.5, We know that mean = np = 3, which means, most likely outcome for gaps located on right side = 3,

So, most likely outcome for located on left = 6-3 =3 .

So, true

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