Question

The monthly utility bill in a city is normally distributed. The mean is $120 and the standard deviation is $25. A utility bill is randomly selected. Answer each of the following questions. (5 points each, total 20 points) (a) Calculate the probability that the utility bill is less than $100. (b) Calculate the probability that the utility bill is between $105 and $125. For each sub-problem, you must show all work to calculate (i) the standardized value and (ii) the probability specified in the problem statement. Your work must contain, but not limited to, probability and inequality notations, graphs, and calculator commands. Round your answer to 4 decimal places if necessary. Select the correct answer and write the letter in the designated box. Show your standardization process for Show your standardization process for part (a). part (b). Select one answer below Select two answers below Standardized Value: Write a calculator command that finds the probability in part (a) Standardized Values: Write a calculator command that finds the probability in part (b) Select one answer below Select one answer below Probability: Probability: This list is designed for all the sub-problems on this page only. A. -0.50 B. -0.60 C. -0.80 D. 0.20 F. 0.74 G. 0.2119 H. 0.7881 I. 0.6950 K. 0.8399 L. 0.3169 E. 0.48 J. 0.3050

Answer 1

a.

$\small \\ P( X < 100) = P\left ( \frac{ X - \mu}{\sigma} < \frac{100 - 120}{25} \right ) \\\\ \\ P(X < 100) = P (z<-0.8) \\\\\\ P(X < 100) = 0.2119$

Standardised value = -0.8

calculator command = normalcdf()

probability = 0.2119

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b.

X- P(105 < X < 125) = P 105 – 120 25 125 - 120 25 P(105 < X < 125) = P(-0.6<:<0.2) P(105< X < 125) = P(: <0.2) - P(:< -0.6) P(105 < X < 125) = 0.5793 – 0.2743 P(105 < X < 125) = 0.3050

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