an english test has 50 multiple - choice questions, each with five answer choices and one correct answer. a…

an english test has 50 multiple - choice questions, each with five answer choices and one correct answer. a student guesses each answer choice randomly. let x represent the number of questions answered correctly. what is the shape of the probability histogram of x?\no skewed left\no skewed right\no approximately uniform\no approximately symmetric

an english test has 50 multiple - choice questions, each with five answer choices and one correct answer. a student guesses each answer choice randomly. let x represent the number of questions answered correctly. what is the shape of the probability histogram of x?\no skewed left\no skewed right\no approximately uniform\no approximately symmetric

Answer

Explanation:

Step1: Identify the distribution

This is a binomial distribution problem. Here, $n = 50$ (number of questions) and $p=\frac{1}{5}= 0.2$ (probability of getting a question correct by guessing).

Step2: Check the conditions for normal - approximation

For a binomial distribution $X\sim B(n,p)$, the normal - approximation $N(np,np(1 - p))$ can be used when $np\geq5$ and $n(1 - p)\geq5$. Calculate $np=50\times0.2 = 10\geq5$ and $n(1 - p)=50\times(1 - 0.2)=40\geq5$.

Step3: Determine the shape

When a binomial distribution $B(n,p)$ can be approximated by a normal distribution $N(np,np(1 - p))$ (as in this case), the probability histogram of the binomial distribution is approximately symmetric.

Answer:

approximately symmetric