Mathematics, 02.11.2020 16:30, leannehounschell

The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively. a An engineering school sets 550 as the minimum SAT math score for new students. What percentage of students will score below 550 in a typical year

Answers: 2

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answered: skifchaofficial01

Complete Question

The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively.

a An engineering school sets 550 as the minimum SAT math score for new students. What percentage of students will score below 550 in a typical year

b What would the engineering school set as a comparable standard on the ACT math test?

$P(X < 550 ) = 75.8 \%$

The minimum for ACT is x = 22.2

Step-by-step explanation:

From the question we are told that

The mean for SAT is $\mu_1 = 480$

The standard deviation for SAT is $\sigma_1 = 100$

The mean for ACT is $\mu_2 = 18$

The standard deviation for $\sigma_2 = 6$

Generally the proportion of students will score below 550 in a typical year is mathematically represented as

$P(X < 550 ) = P(\frac{X - \mu_1 }{\sigma_1} < \frac{550 - 480}{100} )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

P(X < 550 ) = P(Z< 0.7)

From the z table the area under 0.7 to the left is

=> P(Z< 0.7) = 0.75804

P(X < 550 ) = 0.75804

Converting to percentage

P(X < 550 ) = 0.75804 * 100

$P(X < 550 ) = 75.8 \%$

Generally the score which the engineering school would set as a comparable standard on the ACT math test is mathematically evaluated as

$P( X < x) = P(\frac{X - \mu_2 }{\sigma_2} < \frac{x - 18 }{6} ) = 0.75804$

=> $P( X < x) = P(Z < \frac{x - 18 }{6} ) = 0.75804$

From the normal distribution table the critical value of 0.75804 is

z = 0.7

$\frac{x- 18}{6} = 0.7$

=> x = 22.2

answered: Guest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics...