Question

according to a survey, 40% of adults watch a particular television show. six adults are selected at random. the binomial distribution below shows the probability that k out of 6 adults watch the television show.
p(k = 0) = 0.0467
p(k = 1) = 0.1866
p(k = 2) = 0.3110
p(k = 3) = 0.2765
p(k = 4) = 0.1382
p(k = 5) = 0.0369
the distribution is
○ symmetric.
○ skewed.
○ both symmetric and skewed.
done ✔

Explanation:

Step1: Compare symmetric condition

A binomial distribution is symmetric if $p=0.5$. Here, $p=0.4
eq 0.5$.

Step2: Check probability trend

Observe probabilities: they rise to a peak at $k=2$, then fall, with left tail shorter than right tail.

Step3: Classify distribution

Since $p<0.5$, the distribution is right-skewed.

Answer:

skewed.