Respuesta :
Answer:
There are 2 expected readings greater than 2.70 V
Solution:
As per the question:
Total no. of readings, n = 60 V
Mean of the voltage, [tex]\mu = 2.501 V[/tex]
standard deviation, [tex]\sigma = 0.113 V[/tex]
Now, to find the no. of readings greater than 2.70 V, we find:
The probability of the readings less than 2.70 V, [tex]P(X\leq 2.70)[/tex]:
[tex]z = \frac{x - \mu}{\sigma} = \frac{2.70 - 2.501}{0.113} = 1.761[/tex]
Now, from the Probability table of standard normal distribution:
[tex]P(z\leq 1.761) = 0.9608[/tex]
Now,
[tex]P(X\geq 2.70) = 1 - P(X\leq 2.70) = 1 - 0.9608 = 0.0392 = 3.92%[/tex]
Now, for the expected no. of readings greater than 2.70 V:
[tex]P(X\geq 2.70) = \frac{No.\ of\ readings\ expected\ to\ be\ greater\ than\ 2.70\ V}{Total\ no.\ of\ readings}[/tex]
No. of readings expected to be greater than 2.70 V = [tex]P(X\geq 2.70)\times Total\ no.\ of\ readings[/tex]
No. of readings expected to be greater than 2.70 V = [tex]0.0392\times 60 = 2.352[/tex] ≈ 2
