A certain temperature measurement is performed 500 times. The mean value is 0 deg F and the standard deviation is 1 deg F. Assum

Question

6 days ago

12

ing a normal distribution for the error in the measurement, how many readings fall within /- 2.000 deg F of the mean value

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-04-10T03:38:16+03:00

Response:

477

Detailed explanation:

Provided information:

Number of trials (n) = 500

Mean (m) = 0

Standard deviation (s) = 1

how many readings fall within +/- 2.000 deg F of the mean value

Mean of 0 and standard deviation of 1

P(-2 ≤ x ≤ 2)

Utilizing the Z probability calculator:

P(x ≤ 2) = 0.97725;

P(x ≤ - 2) = 0.02275

Thus:

P(x ≤ 2) - P(x ≤ - 2) = 0.97725 - 0.02275 = 0.9545

Accordingly, number of readings in 500 trials:

0.9545 multiplied by 500 equals 477.25

≈ 477 values