An electronics store has received a shipment of 30 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other eighteen have a single slot. Suppose that six of the 30 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? binomial with n = 12, x = 6, and p = 6/12 binomial with n = 30, x = 12, and p = 6/30 hypergeometric with N = 30, M = 12, and n = 6 O hypergeometric with N = 12, M6, and n = 12 (b) Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤2) - P(X ≥ 2) × (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation radios × radios

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.4: Applications
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An electronics store has received a shipment of 30 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other eighteen have a
single slot. Suppose that six of the 30 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the
radios stored under the display shelf that have two slots.
(a) What kind of distribution does X have (name and values of all parameters)?
binomial with n = 12, x = 6, and p = 6/12
binomial with n = 30, x = 12, and p = 6/30
hypergeometric with N = 30, M = 12, and n = 6
O hypergeometric with N = 12, M6, and n = 12
(b) Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.)
P(X = 2) =
P(X ≤2) -
P(X ≥ 2)
×
(c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.)
mean value
standard deviation
radios
×
radios
Transcribed Image Text:An electronics store has received a shipment of 30 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other eighteen have a single slot. Suppose that six of the 30 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? binomial with n = 12, x = 6, and p = 6/12 binomial with n = 30, x = 12, and p = 6/30 hypergeometric with N = 30, M = 12, and n = 6 O hypergeometric with N = 12, M6, and n = 12 (b) Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤2) - P(X ≥ 2) × (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation radios × radios
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