Z
z
1. Find the indicated critical value 0.02 =?
Using a table:
This is the left tailed test critical value, with 0.02 prob.
answer is:
-2.054
2. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. A. Find the probability of a pregnancy lasting 307 days or longer. B. If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
A. The probability that a pregnancy will last 307 days or longer is ?
A:
z = (x-mu)/sigma
Z = (307-267)/15
Z = 2.66667
Prob(z > 2.66667) from a z table:
0.0038
B:
The z value for the lowest 2% is: -2.054
X = z*sigma + mu
X = -2.054*15 + 267
X = 236.19 days
3. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z=0.13 The area of the shaded region is ?
Prob(z < 0.13)
= 0.5517
4. Assume the readings on the thermometers are normally distributed with a mea of 0 celcius and a standard diviation of 1.00 C. Find the probability that a randomly selected thermometer reads greater than -1.99. What is the probability?
z = (x-mu)/sigma
z = (-1.99-0)/1
= -1.99
Prob(z > -1.99) from the table:
0.9767
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