Respuesta :
The probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.
What is the standard deviation?
It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
Given that, a fertilizer manufacturer produces fertilizer in 10-pound bags with a standard deviation of 0.24 pounds per bag, Normally, the bag weights are distributed.
Given the data in the question;
μ= 10-pound bags
standard deviation s= 0.24 pounds
sample size n = 4
Typically, the bag weights are distributed as follows:
p( x' less than 9.8 ) will be;
p( (x'-μ_x' / s_x') < (9.8-μ_x' / s_x') )
As we know that;
μ_x' = μ_x = 10
and s_x' = s_x/√n = 0.24/√4
Put the value as
p( z < ( (9.8 - 10) / (0.24/√4) )
p( z < -0.2 / 0.12 )
p( z < -1.67 )
{ From z-table }
⇒ p( z < -1.67 ) = 0.0475 ≈ 0.05
Thus, the probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.
Learn more about the standard deviation here:
brainly.com/question/12402189
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