Please I need help with these 4 questions 1. According to the Internal Revenue S
ID: 3360688 • Letter: P
Question
Please I need help with these 4 questions
1. According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are between $3000 and 3500?
47.78%
64.61%
46.43%
21.51%
2.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are less than $3000?
32.66%
78.93%
51.53%
67.34%
3.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are less than $3500?
94.51%
88.85%
68.35%
34.90%
4.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are between $2500 and $3500?
29.33%
51.40%
49.77%
75.19%
47.78%
64.61%
46.43%
21.51%
2.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are less than $3000?
32.66%
78.93%
51.53%
67.34%
3.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are less than $3500?
94.51%
88.85%
68.35%
34.90%
4.
According to the Internal Revenue Service, the mean tax refund for a particular year was $2708. Assume that the standard deviation is $650 and that the amounts refunded follow a normal distribution.
What percent of refunds are between $2500 and $3500?
29.33%
51.40%
49.77%
75.19%
Explanation / Answer
Mean = $2708
Standard deviation = $650
P(X < A) = P(Z < (A - mean)/standard deviation)
1) P(3000 < X < 3500) = P(X < 3500) - P(X < 3000)
= P(Z < (3500 - 2708)/650) - P(Z < (3000 - 2708)/650)
= P(Z < 1.22) - P(Z < 0.45)
= 0.8888 - 0.6736
= 0.2152
= 21.51%
2) P(X < 3000) = 0.6736
= 67.34%
3) P(X < 3500) = 0.8888
= 88.85%
4) P(2500 < X < 3500) = P(X < 3500) - P(X < 2500)
= P(Z < (3500 - 2708)/650) - P(Z < (2500 - 2708)/650)
= P(Z < 1.22) - P(Z < -0.32)
= 0.8888 - 0.3745
= 0.5143
= 51.40%