Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 78 and standard deviation 8.2. a. A particular employer requires job candidates to score at least 84 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 84? b. The testing service reported to a particular employer that one of its job candidate's scores fell at the 98th percentile of the distribution (i.e., approximately 98% of the scores were lower than the candidate's, and only 2% were higher). What was the candidate's score? Click here to view a table of areas under the standardized normal curve. a. Approximately % of the test scores during the past year exceeded 84. (Round to one decimal place as needed.) b. The candidate's score was (Round to the nearest whole number as needed.)
Added by Alicia C.
Close
Step 1
The z-score is calculated as: z = (X - μ) / σ where X is the test score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get: z = (84 - 78) / 8.2 ≈ 0.73 Now, we need to find the percentage of test scores that exceeded 84. We can use Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 88 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Although controversial, some human resources departments administer standard IQ tests to potential employees. The Stanford-Binet test scores are well modelled by a Normal model with mean 100 and standard deviation 17. If the applicant pool is well modelled by this distribution, a randomly selected applicant would have what probability of scoring in the following regions? Use the 68-95-99.7 Rule to approximate the probabilities rather than using technology to find the values more precisely. Complete parts a through d. a) What is the probability of scoring 100 or above? b) What is the probability of scoring 151 or above? c) What is the probability of scoring between 66 and 134? d) What is the probability of scoring above 117?
Jason H.
An assessment was given to 1,000 practicing health administrators to measure competency against a set of federal regulations and laws regarding privacy matters and health data. The mean score on the assessment was 64, and the standard deviation was 7.2. A) Calculate the z-score, z = (x - μ)/σ, for a person with a score of 80. B) Assuming a normal distribution, approximately what proportion of candidates would have scores equal to or higher than 80? C) If the assessment required a z-score of 1.5 in order to be deemed proficient, what score must a candidate have earned to pass? D) A candidate earned a z-score of 0.450. What would you tell him about his performance in general terms? E) What proportion of students should be expected to obtain z-scores between +1 and -1?
Varun I.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD