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Pachacha [2.7K]
3 years ago
9

Mr. Helsley wishes to save atleast $1500 in 12 months. If he saved $300 during the first 4 months, what is the least possible av

erage amount that he must save in each of the remaining 8 months ?
Mathematics
1 answer:
faust18 [17]3 years ago
3 0

Answer:he must save an average of $150 or more in each of the remaining 8 months.

Step-by-step explanation:

Mr. Helsley wishes to save at least $1500 in 12 months. If he saved $300 during the first 4 months, then the amount left would be

≥ 1500 - 300

Let x represent the least possible average amount that he must save in each of the remaining 8 months. This means that the total amount that he would save in the last 8 months would be 8x. Therefore,

300 + 8x ≥ 1500

8x ≥ 1500 - 300

8x ≥ 1200

x ≥1200/8

x ≥ 150

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Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day
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The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

<h3>How to calculate the probability distribution?</h3>

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

<h3>Calculation:</h3>

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

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Thus, the required probability is 0.0247.

Learn more about standard normal distribution here:

brainly.com/question/26822684

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