Question

Measurement errors using a certain measuring device are uniformly distributed on the interval
from −5 mm to 5mm.
a. Find the probability that a measurement made with this device is accurate to within ±3 mm.
That is, find the probability that when a measurement is made using this device, the error made
lies in the interval from −3 mm to 3 mm.
b. If 10 items are measured with this device, find the probability that at least 8 are measured
accurately to within ±3 mm. Assume that the measurement errors are independent.

Answer 1

This is a uniform distribution with

Since we know that
Probability density function of a uniform distribution is

This implies that
Cummulative density function of a uniform distribution is

b)
This is a binomial distribution question with
n = 10
p = 0.6
q = 1 - p = 0.4
where


x = 8

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