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Vika [28.1K]
3 years ago
10

The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen

eggs. What is the probability that the mean weight of the eggs in the sample will be less than 2.2 ounces?
Mathematics
1 answer:
n200080 [17]3 years ago
5 0

Answer:

P(\bar X

P(\bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(2.25,\frac{0.2}{\sqrt{12}})

Solution to the problem

We want this probability:

P(\bar X

The best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(\bar X

P(\bar X

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Step-by-step explanation:

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Jess jogs at a rate of 6 miles per hour. The next time she jogs she increases her speed to a rate of 7 mile per hour. How long w
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Answer:

0.86 hour

Step-by-step explanation:

Jess jogs at a rate of 6 miles per hour.

The next time she jogs she increases her speed to a rate of 7 mile per hour.

The new rate of Jess's jogging is 7 miles per hour

How long will it take her to jog 6 miles?

Hence:

7 miles = 1 hour

6 miles = x hours

Cross Multiply

7 × x = 6 × 1

x = 6/7

x = 0.8571428571 hour

Approximately = 0.86 hour

It will take Jess 0.86 hour to jog for 6 miles

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A car requires 22 litres of petrol to travel a distance of 259.6 km.Find
Anon25 [30]

Answer:

Step-by-step explanation:

1. A car requires 22 litres of petrol to travel a distance of 259.6 km

what is the distance that the car can travel on 63 ltr of petrol

22ltr = 259.6km

63ltr=

cross multiply

{63 x 259.6}/22 = 16354.8/22 = 743.4 km

A car requires 22 litres of petrol to travel a distance of 259.6 km, it would require 63 ltr of petrol to travel 743.4km

2. To travel a distance of 2013.2 km

we would need to calculate the amount of fuel

A car requires 22 litres of petrol to travel a distance of 259.6 km

what amount of fuel would it require to travel 2013.2km

22ltr = 259.6km

xltr = 2013.2km

x is the value of petrol to cover 2013.2km

cross multiply

(2013.2 x 22)/259.6

44290.4/259.6 = 170.610169492≈170.6 ltr

A car requires 22 litres of petrol to travel a distance of 259.6 km, it would require 170.6 ltr of petrol to travel 2013.2km

if 1ltr is $1.99

170.6 ltr is (170.6 x 1.99)/1 = $339.494≈$339.5

The price of fuel consumed for 2013.2 km at 1 liter of petrol at $1.99 is $339.5

5 0
3 years ago
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