Answer: 34.13%.
Explanation:
Given : Expected return : [tex]\mu=12\%=0.12[/tex]
Standard deviation: [tex]\sigma=6\%=0.06[/tex]
Let x be the stock returns.
Then, the probability that stock returns between 12% and 18%:
[tex]P(0.12<x<0.18)=P(\dfrac{0.12-0.12}{0.06}<\dfrac{x-\mu}{\sigma}<\dfrac{0.18-0.12}{0.06})\\\\=P(0<Z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=P(Z<1)-P(Z<0)\\\\=0.8413-0.5\ \ \ \text{[By z-table]}\\\\=0.3413[/tex]
Hence, the likelihood that this stock returns between 12% and 18% is 34.13%.
