Mathematics : asked on Valrom
 12.11.2021

Ford and GM pick up trucks are being tested for fuel efficiency, which is commonly measured in miles per gallon (mpg). The fuel efficiency of Ford trucks is found to follow a normal distribution with mean 20 mpg and a standard deviation of 3 mpg. The fuel efficiency of GM trucks is found to follow a normal distribution with mean 24 mpg and standard deviation of 4 mpg. Compute the probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

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24.06.2023, solved by verified expert
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0.7881 = 78.81% probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38 and standard deviation Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38, the zscore of a measure X is given by:

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.

The fuel efficiency of Ford trucks is found to follow a normal distribution with mean 20 mpg and a standard deviation of 3 mpg.

This means that Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

The fuel efficiency of GM trucks is found to follow a normal distribution with mean 24 mpg and standard deviation of 4 mpg.

This means that Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

Compute the probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

This is the probability that the subtraction of ford by gm is less than 0. First, we find the mean and the standard deviation.

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

This probability is the pvalue of Z when X = 0. So

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38

Ford and GM pick up trucks are being tested for, №17887079, 12.11.2021 03:38 has a pvalue of 0.7881

0.7881 = 78.81% probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

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Mathematics
Step-by-step answer
P Answered by PhD

0.7881 = 78.81% probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.

The fuel efficiency of Ford trucks is found to follow a normal distribution with mean 20 mpg and a standard deviation of 3 mpg.

This means that \mu_{F} = 20, \sigma_{F} = 3

The fuel efficiency of GM trucks is found to follow a normal distribution with mean 24 mpg and standard deviation of 4 mpg.

This means that \mu_{G} = 24, \sigma_{G} = 4

Compute the probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

This is the probability that the subtraction of ford by gm is less than 0. First, we find the mean and the standard deviation.

\mu = \mu_{F} - \mu_{G} = 20 - 24 = -4

\sigma = \sqrt{\sigma_{F}^2+\sigma_{G}^2} = \sqrt{3^2+4^2} = 5

This probability is the pvalue of Z when X = 0. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0 - (-4)}{5}

Z = 0.8

Z = 0.8 has a pvalue of 0.7881

0.7881 = 78.81% probability that a randomly chosen Ford truck outperforms a randomly chosen GM truck in terms of fuel efficiency

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Mathematics
Step-by-step answer
P Answered by PhD

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given below

The solution is given below
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 6 gallons =$15

Cost of 1 gallon =15/6

                           =$2.5

Cost of 7 gallons=$2.5 * 7

                           =$17.5

Mathematics
Step-by-step answer
P Answered by PhD

Weight of adult elephant = 24,000 pounds

Weight of baby elephant = 260 pounds

Difference between weight = 24,000 - 260 = 23,740

Adult elephant weights 23,740 pounds more 

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