Exam (elaborations)
STA 2023 Elementary Statistics STA 2023 Test 3 Exam Questions and answers
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- Saint Petersburg College
STA 2023 Elementary Statistics
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ELEMENTARY STATISTICS (STA 2023)TEST 3 (B)
Name___________________________________________
Date__________________
ALL PROBLEMS ARE EQUALLY WEIGHTED
Using the following uniform density curve, answer the question.
1) What is the probability that the random variable has a value greater than 5? 1)
A) 0.500 B) 0.375 C) 0.325 D) 0.250
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
2) 2)
A) 0.2802 B) 0.8599 C) 0.1401 D) 0.7199
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
3) Shaded area is 0.8599. 3)
A) 0.5557 B) 1.08 C) -1.08 D) 0.8051
If z is a standard normal variable ( mean is 0 and standard deviation is 1 ), find the probability.
4) P(z < 0.97) 4)
A) 0.8340 B) 0.8315 C) 0.1660 D) 0.8078
Find the indicated value.
5) z 0.02 5)
A) 1.99 B) 2.05 C) 2.72 D) -2.05
1
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, Assume that X has a normal distribution, and find the indicated probability.
6) The mean is µ = 15.2 and the standard deviation is = 0.9. 6)
Find the probability that X is at least 13.2.
A) 0.9869 B) 0.0131 C) 0.9998 D) 0.2092
Find the indicated probability.
7) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a 7)
standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected
bottle will be less than 32 oz?
A) 0.3821 B) 0.5987 C) 0.0987 D) 0.4013
8) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 8)
200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a
rating that is between 200 and 275.
A) 0.4332 B) 0.0668 C) 0.9332 D) 0.5
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C 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 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. 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.
9) Find P96, the 96th percentile. 9)
A) 1.82° B) 1.03° C) 1.75° D) -1.38°
Solve the problem.
10) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 10)
200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the
probability that their mean is greater than 215.
A) 0.0289 B) 0.1179 C) 0.3821 D) 0.4713
Solve the problem. Round to the nearest tenth unless indicated otherwise.
11) Scores on an English test are normally distributed with a mean of 38.8 and a standard deviation of 11)
6.4. Find the score that separates the bottom 41% from the top 59%.
A) 42.6 B) 37.3 C) 40.3 D) 35.0
Solve the problem.
12) The weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a 12)
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean
weight will be between 15.6 and 21.6 lb?
A) 0.0968 B) 0.3270 C) 0.4032 D) 0.6731
13) Human body temperatures are normally distributed with a mean of 98.20°F and a standard 13)
deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body
temperature is at most 98.50°F.
A) 0.4826 B) 0.9825 C) 0.3343 D) 0.0833
Find the indicated critical z value.
14) Find the critical value z /2 that corresponds to a 98% confidence level. 14)
A) 2.33 B) 2.575 C) 2.05 D) 1.75
2
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