Respuesta :
Answer:
a) 50%
b) 5%
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean distance 60 meters and standard deviation 4 meters.
This means that [tex]\mu = 60, \sigma = 4[/tex]
(a) (2 points) What is the probability that on her first throw, J.v. Lin beats her mean distance?
This is, as a proportion, 1 subtracted by the pvalue of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 60}{4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
1 - 0.5 = 0.5
0.5*100% = 50%
50% probability.
(b) (3 points) The current leader in the Olympics finals has thrown a distance of 66.5 meters. J.V. Lin has one attempt left to beat the leader's throw. What's the probability that Lin beats this throw?
This is 1 subtracted by the pvalue of Z when X = 66.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.5 - 60}{4}[/tex]
[tex]Z = 1.63[/tex]
[tex]Z = 1.63[/tex] has a pvalue of 0.95
1 - 0.95 = 0.05
0.05*100% = 5%
5% probability.
