Answer: 0.1210
Step-by-step explanation:
Given : The length of country and western songs is normally distributed with [tex]\mu=170 \text{ seconds}[/tex]
[tex]\sigma=40\text{ seconds}[/tex]
Sample size : [tex]n=16[/tex]
Let x be the length of randomly selected country song.
z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{158.30-170}{\dfrac{40}{\sqrt{16}}}\approx-1.17[/tex]
The probability that a random selection of 16 songs will have mean length of 158.30 seconds or less by using the standard normal distribution table will be
= [tex]P(x\leq158.30)=P(z\leq-1.17)[/tex]
[tex]=0.1210005\approx0.1210[/tex]
Hence, the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less is 0.1210
