Answer:
0.0668 or 6.68%
Step-by-step explanation:
Mean time (μ)= 46 minutes
Standard deviation (σ) = 6 minutes
The z-score for any given time X is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 37:
[tex]z=\frac{37-46}{6}\\ z=-1.5[/tex]
A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution. The probability that it will take less than 37 minutes to complete the test is
[tex]P(X\leq 37) = 0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
