Probabilidad

González Ramírez Cristina.
Vázquez Preciado Sergio Edgar.

Ejercicio 2. Probabilidad.

1. If scores are normally distributed with a mean of 35 and a standard deviation of 10, what percent ofthe scores is:

a. greater than 34? 53.98%
b. smaller than 42? 75.8%
c. between 28 and 34? 21.82%

2. What are the mean and standard deviation of the standard normal distribution?

a) m =0 ; sd = 1
b) m = 75 ; sd = 83

3. The normal distribution is defined by two parameters. What are they?

Media y desviación estándar.

4. (a) What proportion of a normal distribution iswithin one standard deviation of the mean? 68%
(b) What proportion is more than 2.0 standard deviations from the mean? 95%
(c) What proportion is between 1.25 and 2.1 standard deviations above themean? 8.77%

5. A test is normally distributed with a mean of 70 and a standard deviation of 8.
(a) What score would be needed to be in the 85th percentile? 78.29
(b) What score would be neededto be in the 22nd percentile? 63.82

6. Assume a normal distribution with a mean of 70 and a standard deviation of 12. What limits would include the middle 65% of the cases? 58.78 y 81.21

7.A normal distribution has a mean of 20 and a standard deviation of 4. Find the Z scores for the following numbers:

(a) 28 = 2
(b) 18 = -0.5
(c) 10 = -2.5
(d) 23 = 0.75

8. Assume thespeed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is theproportion of vehicles less than or equal to the speed limit? > pnorm(65,mean=71,sd=8) [1] 0.2266274 22.66%
b. What proportion of the vehicles would be going less than 50 mph? 0.04% >pnorm(50,mean=71,sd=8) [1] 0.004332448
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion? 73 mph...