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goblinko [34]
3 years ago
6

In a store, a sample of 60 pens was selected from a box of 1,200 pens. Of these 60, 4 pens did not work. About how many pens cou

ld be expected to not work in the group of 1,200 pens?
Mathematics
1 answer:
Lapatulllka [165]3 years ago
3 0
Ok so if 1200 total pens and 60 were taken that's a ratio of 1200/60=20

out of 60pens 4 didn't work, again ratio is 4/60=1/15 so about 1/15 of the pens didn't work. 

so we have 1200pens * 1/15broken ratio = 80 pens or we can say 

20*4=80pens won't work from 20 groups of 60 and 4 out of 60 not working is 20*4=80 not working from total batch of 1200.

hope this helps you some! thank you!!!!!!!!!
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Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

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From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

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Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

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Step-by-step explanation:

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