Respuesta :
Answer:
The probability that the maximum speed is at most 49 km/h is 0.8340.
Step-by-step explanation:
Let the random variable X be defined as the maximum speed of a moped.
The random variable X is Normally distributed with mean, μ = 46.8 km/h and standard deviation, σ = 1.75 km/h.
To compute the probability of a Normally distributed random variable we first need to convert the raw score of the random variable to a standardized or z-score.
The formula to convert X into z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Compute the probability that the maximum speed is at most 49 km/h as follows:
Apply continuity correction:
P (X ≤ 49) = P (X < 49 - 0.50)
= P (X < 48.50)
[tex]=P(\frac{X-\mu}{\sigma}<\frac{48.50-46.80}{1.75})\\=P(Z<0.97)\\=0.83398\\\approx 0.8340[/tex]
*Use a z-table for the probability.
Thus, the probability that the maximum speed is at most 49 km/h is 0.8340.
