Hi i am doing my stats homework and have no idea how to do this problem. If some

Question

Hi i am doing my stats homework and have no idea how to do this problem. If someone could please help me answer it and show steps so i can understand.

2. The Test of Euglish as a Foreign language TOEFL) is required by moet universities to help ia their aduaission of iuternatioual s dents Froua past records at a certain university, these scores are a pproximately normal distributed with a mean of 125 and a standard deviation of If an international student's application is selected at (a) What the probability that the student's TOEFL score is at most 13? 5 points. b) What is the probability that the student's TOEFL score is greater than 410? 5 points. c) What is the probability that the student's TOEFL score is between 350 and 5 points,

Explanation / Answer

Sol:

its problem on normal distribution

mean=425

std deviation=50

atmost means less than or equal to

need to find

P( X<=430) conver X to Z variable

Z=x-mean/stddev

=430-425/50

=5/50

=1/10

=0.1

P (X<430)=P (Z<0.1)

Step 3: Use the standard normal table to conclude that:

P (Z<0.1)=0.5398

ANSWER 0.5398

SOLUTIONB:

P(X >440)

z=440-425/50

=15/50

=0.3

P ( Z>0.3 )=1P ( Z<0.3 )=10.6179=0.3821

ANSWER: 0.3821

sOLUTIONC:

ince =425 and =50 we have:

P ( 350<X<500 )=P ( 350425< X<500425 )=P ( 350425/50<X/<500425/50)

Since Z=x/ , 350425/50=1.5 and 500425/50=1.5 we have:

P ( 350<X<500 )=P ( 1.5<Z<1.5 )

To find the probability of P (1.5<Z<1.5), we use the following formula:

P (1.5<Z<1.5 )=P ( Z<1.5 )P (Z<1.5 )

Step 3: P ( Z<1.5 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<1.5 )=0.9332.

Step 4: P ( Z<1.5 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=1.5 we have:

P ( Z<1.5)=1P ( Z<1.5 )

P ( Z<1.5 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<1.5 )=0.9332 so,

P ( Z<1.5)=1P ( Z<1.5 )=10.9332=0.0668

At the end we have:

P (1.5<Z<1.5 )=0.8664

ANSWER :0.8664

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