Step 1a

Identify n,p,q,x

Explanation: number of experiments n = 10

Probability of success p = 0.15

Probability of failures q = 1-p = 1-0.15 = 0.85

number of successful trials x = 4

Step 1b

Calculate Probability P(x)

Explanation: \$n_(C_x) = (n!)/((n-x)!x!)\$

\$10_(C_4) = (10!)/((10-4)!4!)\$ \$=> (10!)/(6! 4!)\$

\$10_(C_4) =210\$

P(x)=\$n_(C_x) p^x q^(n-x)\$

\$P(x=4) = 210 × 0.15^4 × 0.85^(10-4)\$

\$P(x=4) = 210 × 0.15^4 × 0.85^6\$

\$=> 210 ×0.0005 × 0.3771\$

\$P(x=4) = 0.04\$

The probability that exactly 4 candies in a box are pink is 0.04.

⇒ When p > 0.5, the distribution is skewed to the left.

Step 1c

Calculate mean \$\mu\$ and variance \$\sigma^2\$

Explanation:

Mean \$\mu\$ = np = 10 × 0.15

Mean \$\mu\$ = 1.5

Variance \$\sigma^2\$ = npq = 10 × 0.15 × 0.85

Variance \$\sigma^2\$ = 1.275