Please answer all the three a,b, and c part of the question with all the steps t

Question

Please answer all the three a,b, and c part of the question with all the steps to solve. Thanks in advance.

a) What z score does this represent? b) If the mean score on the exam is 82. what is the standard deviation 8. If students is distributed with a mean of 24.3 and a the age of LaGuardia normally standard deviation is 3.6 years answer the following: 120 ptsl a) What is the probability that a student's age is What is the probability that a student's age is greater than 18 years? less then 29 years? b) What is the age of students with the following z scores? 1.24 .85

Explanation / Answer

mean = 24.3 , std. deviation = 3.6

a) P(X < 29 )

By central limit theorem,

P(X < 29 ) = ( 29 - 24.3) / 3.6

= 1.30

We need to find P (Z < 1.30) by using z standard right tail we get,

P(Z <1.30) = 0.9041

P(X > 18 )

By central limit theorem,

  P(X >18 ) = ( 18 - 24.3) / 3.6

= -1.75

We need to find P (Z > -1.75) by using z standard right tail we get,

P(Z <1.30) = 0.9599

b) z score = -0.85

By central limit theorem,

- 0.85 = ( X - 24.3) / 3.6

X - 24.3 = -3.06

X = 21.24

Z score = 1.24

  By central limit theorem,

1.24 = ( X - 24.3) / 3.6

X - 24.3 = 4.464

  X = 28.764

c) P (22 <X <27 )

   By central limit theoerem,

   P( 22 - 24.3 / 3.6 < Z < 27 - 24.3 / 3.6)

  = P( - 0.64 < Z < 0.75)

= 0.5119

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---