Question
Can you please show the steps and mention the name of the theorems you are using thanks!
Suppose that an electronic temperature sensor for fluids (including plasmas, gases, and liquids) obtains temperatures by rand
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Answer #1

Solution: Given that μ = 180, σ = 6

a) for n = 25
P(179 < X < 181) = P((179-180)/(6/sqrt(25)) < (x-μ)/(σ/sqrt(n)) < (181-180)/(6/sqrt(25)))
= P(-0.8333 < Z < 0.8333)
= P(Z < 0.8333) − P(Z < −0.8333)
= 0.7967 - 0.2033
= 0.5934 (rounded)

=> P(Z < 0.8333) can be found by using the following standard normal table:

b) P(Z >= z) = 0.99 => z = 2.33

X = μ + z*σ
= 180 + 2.33*6
= 193.98



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