1.) An archer can hit the bullseye of a target with an accuracy rate of 83%. Arrows hitting the bullseye are independent of each other. The archer is about to take 6 shots. Let X=the number of arrows (out of 6) that hit the bullseye. Describe the shape of the distribution, center, and spread of the distribution of X.
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Given,
The Probability of hitting target is 0.83.
Each trail is independent of each other.
The archer is taking 6 trails.
The random variable is number of arrow that hit.
Hence, It follows binomial distribution with parameters n = 6 and p = 0.83
Shape of the distribution is,
Shape of the distribution is completely depends on n and p.
i) When n is small and p small then distribution is positive skewed. That means mean of the distribution falls in smaller number.
ii) When n is small and p is large then distribution is negatively skewed. That means mean of the distribution falls in greater number. That's the left skewed.
iii) When n is small/large but if p approximately equal to 0.5 then the probability mean of the distribution is falls in center of the numbers. That's why it is symmetric distribution.
iv) When n is large and p is large/small, Then distribution is symmetric about mean and mean falls corresponding to p, if p is large then mean is large and if p is small then mean is small.
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