Math 136 - Introduction to Statistics » Fall 2021 » QUIZ 5 NORMAL DISTRIBUTION

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Question #1
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below (denoted by negative numbers) and some give readings above (denoted by positive numbers). Assume that the mean reading is and the standard deviation of the readings is Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. Find P96, the 96th percentile
A.   1.82°
B.   -1.38°
C.   1.75°
D.   1.03°
Question #2
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below (denoted by negative numbers) and some give readings above (denoted by positive numbers). Assume that the mean reading is and the standard deviation of the readings is Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. Find Q3Q3, the third quartile.
A.   0.53°
B.   0.67°
C.   -1.3°
D.   0.82°
Question #3
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of  at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below  (denoted by negative numbers) and some give readings above  (denoted by positive numbers). Assume that the mean reading is  and the standard deviation of the readings is  Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.
A.   1.39°
B.   1.26°
C.   1.34°
D.   1.45°
Question #4
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below (denoted by negative numbers) and some give readings above (denoted by positive numbers). Assume that the mean reading is and the standard deviation of the readings is Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. Find z0.005.
A.   2.575
B.   2.015
C.   2.835
D.   2.535
Question #5
Solve the problem. Round to the nearest tenth unless indicated otherwise. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find , which is the consumption level separating the bottom 45% from the top 55%.
A.   1021.7
B.   1148.1
C.   1087.8
D.   1078.3
Question #6
Solve the problem. Round to the nearest tenth unless indicated otherwise. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find , the score which separates the lower 60% from the top 40%.
A.   207.8
B.   211.3
C.   187.5
D.   212.5
Question #7
Assume that X has a normal distribution, and find the indicated probability. The mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than 53.0.
A.   0.9599
B.   0.0802
C.   0.5589
D.   0.0401
Question #8
Assume that X has a normal distribution, and find the indicated probability. The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 17.
A.   0.9772
B.   0.9713
C.   0.9821
D.   0.0228
Question #9
Assume that X has a normal distribution, and find the indicated probability. The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 15.2.
A.   0.5000
B.   0.0003
C.   1.0000
D.   0.9998
Question #10
Assume that X has a normal distribution, and find the indicated probability. The mean is μ= 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1.
A.   0.8413
B.   0.1550
C.   0.1357
D.   0.1587

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