Question

Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.244°C and 0.251°C.

P(0.244<Z<0.251)

Answer 1

Here in this scenario we have given that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

A single thermometer is randomly selected and tested. the probability of obtaining a reading between 0.244°C and 0.251°C is computed using following formula and steps,

The following information has been provided: M = 0, 0 =1 We need to compute Pr(0.244 < X < 0.251). The corresponding z-values needed to be computed are: X1 - u 0.244 - 0 Z1 = = 0.244 O o 1 X2 – u 0.251 – 0 22 = - 0.251 0 1 Therefore, we get: = Pr(0.244 < X < 0.251) = Pr (0:241 0.244 - 0 0.251 – 0 <<< = Pr(0.244 < Z < 0.251) 1 T - = Pr(Z < 0.251) – Pr(Z < 0.244) = 0.5991 – 0.5964 = 0.0027 The following is obtained graphically: Standard Normal Distribution: Pr(0.244<Z<0.251)=0.0027 O 0.40 0.35 0.30 0.25 0.20 0.15 0.10 O 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

The probability is calculated using Standerd normal z-table or using Excel.

The probability that A single thermometer is randomly selected and tested. the probability of obtaining a reading between 0.244°C and 0.251°C is 0.0027

P(0.244<Z<0.251) = 0.0027.

Thank you.