Question

In a recent survey of 655 working Americans ages 25-34, the average weekly amount spent on lunch was $44.60 with a standard deviation of $2.81. The weekly amounts are approximately bell- shaped.
a. Estimate the percentage of amounts that are between $36.17 and $44.60.
b. Estimate the percentage of amounts that are between $41.79 and $47.41.
c. Estimate the percentage of amounts that are at least $38.98.
d. Between what two values will approximately 95% of the amounts be?

Answer 1

Answer:

a) the percentage of amounts that are between $36.17 and $44.60 is 49.87%

b.) Therefore  the percentage of amounts that are between $41.79 and $47.41 is 68.27%

c)  Therefore percentage of amounts that are at least $38.98 = 97.72%

d) The two values will approximately 95% of the amounts be $39.1 and $50.1

Step-by-step explanation:

i) In a recent survey of 655 working Americans, ages 25 - 34, the average weekly amount spent on lunch was $44.60 with a standard deviation of $2.81

ii) mean = $44.60

iii) standard deviation = $2.81

a) Estimate the percentage of amounts that are between $36.17 and $44.60.

   therefore we have to find P($36.27 < X < $44.60) or

P(( (36.17 - 44.60)/2.81) < z < ( (44.60 - 44.60)/2.81)) = P(-3 < Z < 0)

  therefore P(-3 < Z < 0) = P(Z < 0) - P( Z < -3) = 0.4987

 Therefore  the percentage of amounts that are between $36.17 and $44.60 is 49.87%

b)estimate the percentage of amounts that are between $41.79 and $47.41.

P($41.79 < X < $47.41) or

P(( (41.79 - 44.60)/2.81) < z < ( (47.41 - 44.60)/2.81)) = P(-1 < Z < 1)

  therefore P(-1 < Z < 1) = P(Z < 1) - P( Z < -1) = 0.6827

 Therefore  the percentage of amounts that are between $41.79 and $47.41 is 68.27%

c)Estimate the percentage of amounts that are at least $38.98.

   therefore we have to find

     P(X ≥ $38.98) or

    P(z ≥ (38.98 -  44.6)/2.81 ) = P( Z  ≥  -2)

  therefore we have to find 1 - P(Z < -2) = 1 - 0.0228 = 0.9772

 

Therefore percentage of amounts that are at least $38.98 = 97.72%

d.) Between what two values will approximately 95% of the amounts be?

The two values will approximately 95% of the amounts be $39.1 and $50.1