The average annual amount American households spend for daily transportation is $6312. Assume that the amount spent is normally distributed. Suppose you learn 5% of households spend less than $1000 for daily transportation. What is the standard deviation of the amount spent?
What is the probability that a household spends between $4000 and $6000?
Can you please help me with these two problems? I don't understand how to do them so any help would be greatly appreciated.
What is the probability that a household spends between $4000 and $6000?
Can you please help me with these two problems? I don't understand how to do them so any help would be greatly appreciated.
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z-score for bottom 5% = -1.645 [ reading from a z-table ]
6312 - 1.645*SD = 1000
SD = (6312-1000)/1.645 = $3229 <-------
z1= (4000-6312)/3229 = -0.716 , z2 = (6000 - 6312)/3229 = - 0.097
P(-0.716 < z < - 0.097) = 0.2244 <-------
[ or if you don't interpolate , P(-0.72 < z < - 0.1) = 0.2602 ]
6312 - 1.645*SD = 1000
SD = (6312-1000)/1.645 = $3229 <-------
z1= (4000-6312)/3229 = -0.716 , z2 = (6000 - 6312)/3229 = - 0.097
P(-0.716 < z < - 0.097) = 0.2244 <-------
[ or if you don't interpolate , P(-0.72 < z < - 0.1) = 0.2602 ]