Question

# Standard Normal Distribution – In Exercises 9 – 13, assume that thermometer readings are normally distributed...

Standard Normal Distribution – In Exercises 9 – 13, assume that thermometer readings are normally distributed with a mean of 0oC and a standard deviation of 1.00oC. A thermometer is randomly selected and tested, find the probability of each reading. (The given values are in Celsius degrees.) If using technology instead of Table A-2, round answers to four decimal places.

9. Less than 2.39

10. Greater than 1.35

11. Between 0.14 and 2.57

12. Between -2.33 and 1.33

13. Less than -1.55 and Greater than 2.53

Finding Probability - In Exercises 14 and 15, assume that thermometer readings are normally distributed with a mean of 0oC and a standard deviation of 1.00oC. A thermometer is randomly selected and tested, find the indicated probability, where z is the reading in degrees.

14. P(z < 2.50)

15. P(z < -1.88 or z > 1.88)

Solution :

Using standard normal table,

9)

P(z < 2.39) = 0.9916

Probability = 0.9916

10)

P(z > 1.35) = 1 - P(z < 1.35) = 1 - 0.9115 = 0.0885

Probability = 0.0885

11)

P(0.14 < z < 2.57) = P(z < 2.57) - P(z < 0.14) = 0.9949 - 0.5557 = 0.4392

Probability = 0.4392

12)

P(-2.33 < z < 1.33) = P(z < 1.33) - P(z < -2.33) = 0.9082 - 0.0099 = 0.8983

Probability =  0.8983

13)

P(z < 2.50) = 0.9938

Probability = 0.9938

14)

P(z < -1.88 or z > 1.88)

= P(z < -1.88) + 1 - P(z < 1.88)

= 0.0301 + 1 - 0.9699

= 0.0301 + 0.0301

= 0.0602

Probability = 0.0602

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