Unformatted text preview: Homework: Chapter 5 Page 255 5. Voltages are uniform across 6- 12 volts. Find the probability that the voltage is greater than 10 volts.
Soln: We note that the range of the distribution is 12—6 volts, or six volts. So each volt difference is 116, i.e. as it is uniform, any one volt interval
has a U6 probability of occurring. Now greater than 10 volts is a
difference of two volts, so the probability is U3 or 33%. 7. Between 7 and 10 volts: Same as above, but now the interval is3 volts, or '/2
(50%). 9 0. Normally distributed, mean of 0 and standard deviation of 1. What is probability a
thermometer reading something less than -0.25. We ﬁrst find the z score, and then use the table for the normal distribution. Z = (Jr-ﬂ)
Z = (—0.254)
z = —0.25 We should have noted from the start that these thermometers follow the standard
distribution, so the reading at critical value is the z score! Now we look at the negative 2
table and ﬁnd the value: 0.4013. This means the probability that the thermometer will measure -0.25 or lower is about 40%. ll . . . .
&. Less than 0.25. This is the same problem, Just use the posmve Side of the table: 0.5987, or about 60% of the time it will read 2.5 degrees or less. Page 263 1. Assume IQ scores normally distributed mean 100 and standard deviation of 15.
Find probability that a randomly selected adult has an IQ less than 1 15. Here this
is not the standard normal distribution, so the z score is required. Using this, _ 115 —100 _1 15
So now we want less than, i.e. area to left, and we get from the table, about 0.8413 or 84%. Z 2. Same problem, but greater than 131.5
_ 131.5 “100 _ 15 2.] Z ...
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