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3 years ago

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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?

1 answer:

Alex_Xolod [135]3 years ago

5 0

Answer:

(a) $0.15731$

(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)

= $P(\frac{166.5-166}{0.5}$

= $P(1$

= $P(Z$

$=0.99865-0.84134$

$=0.15731$

(b)

$P(X>167)=P(Z>\frac{167-166}{0.5})$

$=P(Z>2)$

$=1-P(Z$

$=1-0.97725$

$=0.02275$

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