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aliya0001 [1]
3 years ago
7

3. In determining food spending, it was found that the average meal in Albany is normally distributed, with a mean of $40 and a

standard deviation of $4. Find the following: P(X < 40), P(38 < X < 42), P(X > 35), P(X > 51). Find a meal cost which happen to be cheaper than 10% of the meals based on a given data. Find a meal cost which happen to be in the 5% of the most expensive based on a given data. Find a meal costs which happen to be 40% symmetrically around the mean value based on a given data.
Mathematics
1 answer:
Zarrin [17]3 years ago
7 0

Answer:

a) P(X < 40) = 0.5

b) P(38 < X < 42) = 0.69143

c) P(X > 35) = 0.89435

d) P(X > 51) = 0.0029798

e) Find a meal cost which happen to be cheaper than 10% of the meals based on a given data. = $34.872

f) Find a meal cost which happen to be in the 5% of the most expensive based on a given data = $33.42

g) Find a meal costs which happen to be 40% symmetrically around the mean value based on a given data. = $38.988

Step-by-step explanation:

Z score formula = Z score = x - μ/σ

Mean = $40

Standard deviation = $4

a) P(X < 40)

Z score = x - μ/σ

= 40 - 40/4

= 0

Determining the Probability value from Z-Table:

P(X < 40) = 0.5

b) P(38 < X < 42)

For X = 38

Z score = x - μ/σ

= 38 - 40/4

= -0.5

Determining the Probability value from Z-Table:

P(X = 38) = 0.30854

For X = 42

Z score = x - μ/σ

= 42 - 40/4

= 4

Determining the Probability value from Z-Table:

P(x = 42) = 0.99997

Hence, P(38 < X < 42)

P(X = 42) - P(X = 38)

0.99997 - 0.30854

= 0.69143

c) P(X > 35)

Z score = x - μ/σ

= 35 - 40/4

= -1.25

Determining the Probability value from Z-Table:

P( X < 35) = 0.10565

P( X > 35) = 1 - P(X < 35)

1 - 0.10565

= 0.89435

d) P(X > 51)

Z score = x - μ/σ

= 51 - 40/4

= 2.75

Determining the Probability value from Z-Table:

P( X < 51) = 0.99702

P(X > 51) = 1 - P(X < 51)

= 1 - 0.99702

= 0.0029798

e) Find a meal cost which happen to be cheaper than 10% of the meals based on a given data.

z score for 10th percentile = -1.282

Z score formula = Z score = x - μ/σ

Mean = $40

-1.282 = x - 40/4

-1.282 × 4 = x - 40

-5.128 + 40 = x

$34.872

The meal cost which happen to be cheaper than 10% of the meals based on a given data is $34.872

f) Find a meal cost which happen to be in the 5% of the most expensive based on a given data

Z score for 5th percentile = -1.645

Z score formula = Z score = x - μ/σ

Mean = $40

-1.645 = x - 40/4

-1.645 × 4 = x - 40

-6.58 + 40 = x

$33.42

The meal cost which happen to be in the 5% of the most expensive based on a given data is $33.42

g) Find a meal costs which happen to be 40% symmetrically around the mean value based on a given data.

Z score for 40th percentile = -0.253

Z score formula = Z score = x - μ/σ

Mean = $40

-0.253 = x - 40/4

-0.253 × 4 = x - 40

-1.012 + 40 = x

$38.988

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