Answer: 0.9147
Step-by-step explanation:
Given: 20% of the plants ordered are petunias.
Let p = 20% = 0.2
Sample size: n = 120
If they follow normal distribution, then mean = np = 120x 0.2 = 24
Standard deviation = [tex]\sqrt{n p(1-p)}=\sqrt{120\times0.2\times.8}[/tex]
[tex]=\sqrt{19.2}\\\\ =4.38[/tex]
The  probability that no more than 30 plants are petunias : [tex]P(\dfrac{X-\mu}{\sigma}\leq \dfrac{30-24}{4.38})[/tex]
[tex]=P(Z<1.37)= 0.9147[/tex]
Hence, the probability that no more than 30 plants are petunias = 0.9147
