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jay555538
29.06.2021 •
Mathematics
Measurement error that is normally distributed with a mean of 0 and a standard deviation of 0.5 gram is added to the true weight of a sample. Then the measurement is rounded to the nearest gram. Suppose that the true weight of a sample is 166.0 grams.
(a) What is the probability that the rounded result is 167 grams?
(b) What is the probability that the rounded result is 167 grams or more?
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Ответ:
(a)![0.15731](/tpl/images/1385/8936/630d2.png)
(b)0.02275
Step-by-step explanation:
We are given that
Mean=0
Standard deviation=0.5 g
True weight of a sample=166 g
Let X denote the normal random variable with mean =166+0=166
(a)
P(166.5<X<167.5)
=![P(\frac{166.5-166}{0.5}](/tpl/images/1385/8936/d3ba5.png)
=![P(1](/tpl/images/1385/8936/da887.png)
=![P(Z](/tpl/images/1385/8936/8ac86.png)
(b)
Ответ: