The document contains examples of calculating probabilities using the normal distribution. It provides the mean (M), standard deviation (σ), and test values (X) for 5 exercises, then shows the calculations to find the z-score and probability for each test value. The exercises demonstrate how to calculate the probability that a value is above or below the mean, or between two values, for different normal distributions.

1. EJERCICIO #1:
M= 6.3 Z=X-M/ 𝜎
𝜎=0.7
a) P(1<=7.6)=7.6.-6.3/.7=1.3/.7=1.85=.96784
b) 1-.96784
200-x=193.568
c) 4/.7= .2/.7= .28= .61026
d) M= 5%=.5
EJERCICIO #2:
M= 1.7
𝜎= 0.1
a) P(>=1.7 y 1.9)
Z= 1.7-1.7/.1= 0= .5
Z= 1.9-1.7/.1= .2/.1= 2= .97725
b) Z=1.7-1.5/.1=.2/.1=.5
1-.5
500-X?=25,000
EJERCICIO #3:
M= 25
𝜎 =5
X=a) 30, b) 20,c) 22,d) 22,28
a) Z=30-25/5=1=.84134
b) Z=20-25/5=-1=.15866
c) Z=22-25/5=-.6=.27425

2. d) Z=28-25/5=.6=.75804
EJERCICIO #4:
M= 90km/hr
Z=5 km/hr
X=A) P<100, B) P>80, C) P (85,95)
a) Z=100-90/8=1.25=.89435
b) Z= 80-90/8=-1.25=10565
c) Z= 85-90/8=-.62=.26763
Z= 95-90/8= .62= 73237
EJERCICIO #5:
MARCA E
M= 8.5 Z=8.25-8.5/.5= -0.5
𝜎 =.5
X=8.25
MARCA D
M= 8.2 Z=8.4-8.2/.4=0.5=0.69146
𝜎 =.4
X=8.4