Respuesta :
a. Hence in first case, if the distribution is normal, Probability is 0.0077 that the sample mean hardness for a random sample of 16 pins is at least 51
b. In second, Probability is 0 that the sample mean hardness for a random sample of 44 pins is at least 51.
What is mean?
The mean is one of the measures of central tendency used in statistics. The average of the specified collection of numbers is what is referred to as mean. It indicates the data set's values that are distributed equally. The three most popular methods for determining central tendency are the mean, median, and mode.
To find the mean, tally up all the values listed on a datasheet, then divide that total by the total number of values. When all the values are organized in ascending order, the median is the value that falls in the middle of the data. The number in the list that is repeated a maximum number of times is the mode.
a)
Y ~ N ( µ = 50 and σ = 1.6 )
P ( Y > 51 ) = 1 - P ( Y < 51 )
Standardizing the value
Z = ( Y - µ ) /( σ / √(n))
Z = ( 51 - 50 ) /( 1.6 / √ ( 15 ) )
Z = 2.4206
P ( ( Y - µ ) /( σ / √ (n)) > ( 51 - 50 ) /( 1.6 / √(15) )
P ( Z > 2.42 )
P ( Y > 51 ) = 1 - P( Z < 2.42 )
P ( Y > 51 ) = 1 - 0.9923 ( from the Z table)
P ( Y > 51 ) = 0.0077
b)
P ( Y > 51 ) =1 - P ( Y < 51 )
Standardizing the value
Z = ( Y - µ ) /( σ / √(n))
Z = ( 51 - 50 ) /( 1.6 / √ ( 43 ) )
Z = 4.1
P ( ( Y - µ ) /( σ / √ (n)) > ( 51 - 50 ) / ( 1.6 / √(43) )
P ( Z > 4.1 )
P ( Y > 51 ) =1 - P ( Z < 4.1 )
P ( Y > 51 ) = 1 - 1
P ( Y > 51 ) = 0
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