SOLUTION: 1. If the random variable z is the standard normal score, is it true that P(-3 < z < 3) > 1? Why or why not? 2. Givent a binomial distribution with n = 29 and p = 0.83, would

Algebra ->  Probability-and-statistics -> SOLUTION: 1. If the random variable z is the standard normal score, is it true that P(-3 < z < 3) > 1? Why or why not? 2. Givent a binomial distribution with n = 29 and p = 0.83, would       Log On


   



Question 364479: 1. If the random variable z is the standard normal score, is it true that P(-3 < z < 3) > 1? Why or why not?

2. Givent a binomial distribution with n = 29 and p = 0.83, would the normal distribution provide a reasonable approximation? Why or why not?

3. Find the area under the standard normal curve for the following: a). P(z < -0.25) b). P(0.55 < z < 0) c.) P(-1.91 < z < 1.06)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) P%28z%29=int%28p%28x%29%2Cdx%2C-infinity%2Cz%29
int%28p%28z%29%2Cdz%2C-infinity%2Cinfinity%29=1
So P can never be greater than 1.
.
.
2)
The binomial distribution is approximated by a normal distribution for any fixed p(even if p is small) as n is taken to infinity.
.
.
3) P%28z%3C0.25%29=P%280.25%29
.
.
+P%280.55+%3C+z+%3C+0%29=P%280.55%29-P%280%29
P%280.55+%3C+z+%3C+0%29=P%280.55%29-0.5
.
.
+P%28-1.91+%3C+z+%3C+1.06%29=P%281.06%29-P%28-1.91%29