BCC Normal Probability and Standard Deviation Question

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i have 8 probability questions that i need help with. i will post the questions in a minute

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The customer service center in a large New York department store has determined that the
amount of time spent with a customer about a complaint follows a normal distribution, with a
mean of 9.3 minutes and a standard deviation of 2.5 minutes.
Let X = amount of time spent with a customer about a complaint (in minutes).
a) 𝜇 =
b) 𝜎 =
c) What is the standard score (or z-score) for x = 4.3 minutes? Answer: z =
d) What is the standard score (or z-score) for x = 14.3 minutes? Answer: z =
e) Based on the empirical rule, approximately what percent of customers spent between 4.3
minutes and 14.3 minutes with the customer service center regarding a complaint?
Question 2
Let X represent the cost of a Smart LED TV. Which probability expression represents the
following statement?
The probability that a Smart LED TV costs no more than $350
Question 3
Can two events that are mutually exclusive occur at the same time?
Question 4
47% of an insurance agent’s clients have life insurance, 42% have auto insurance, and 21%
have both policies. What is the probability that a randomly selected client has life
insurance or auto insurance?
(Write the probability answer as an exact decimal.)
Question 5
Bonus Question
A box contains ten balls, numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
If you randomly select one ball, do not replace it in the box, and then, select a second ball,
what is the probability that both balls are odd?
Question 6
A box contains ten balls, numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Write each answer as a decimal.
If you randomly select one ball, find the probability that the number is:
a) an odd number
b) at least 6.
c) less than 10.
d) not 3.
e) less than 4 or a multiple of 3.
Question 7
In a batch of 140 calculators, 3 are found to be defective. Estimate the probability that a
randomly selected calculator is not defective.
(Write the answer as a decimal rounded to the nearest hundredth.)
Question 8
The mean time taken to learn the basics of a word processor by a group of students is 200
minutes with a standard deviation of 20 minutes. According to Chebyshev’s Theorem,
what is the minimum probability that a randomly selected student took between 140 and
260 minutes to learn the basics of the word processor?

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Tags:
standard deviation

normal probability

standard score

amount of time spent

estimate the probability

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