Unit Normal Distribution
Consider a tech company with a fruit logo designs a computer circuit where the signal wavelengths form a normal distribution with a standard deviation of 1.25 and a mean of 5. If a random signal is selected, what is the probability its wavelength will be more than 6 wavelengths long?
Expand Hint
For any normal distribution, the table for the unit normal distribution can be utilized via the following transformation:
$$$z=\frac{x-\mu }{\sigma }$$$
where
$$z$$
is the “Z” score associated with the unit normal distribution table,
$$\mu$$
is the mean,
$$\sigma$$
is the standard deviation, and
$$x$$
is the desired region under the bell curve.
Hint 2
$$$z=\frac{x-\mu }{\sigma }=\frac{6-5}{1.25}=0.8$$$
For any normal distribution, the table for the unit normal distribution can be utilized via the following transformation:
$$$z=\frac{x-\mu }{\sigma }$$$
where
$$z$$
is the “Z” score associated with the unit normal distribution table,
$$\mu$$
is the mean,
$$\sigma$$
is the standard deviation, and
$$x$$
is the desired region under the bell curve.
$$$z=\frac{x-\mu }{\sigma }=\frac{6-5}{1.25}=0.8$$$
Referring to the Unit Normal Distribution Table like the one in the FE Handbook:
The left most column contains all the possible values for Z. The red horizontal highlight refers to the the problem’s calculated Z score of 0.8. Because the problem statement asks to include all signals longer than 6 wavelengths on the distribution, the
$$R(x)$$
column is also highlighted in red. The intersecting value of these two row/column is 0.2119, which is the probability of a signal with more than 6 wavelengths being randomly selected.
0.2119
Time Analysis
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