Question

Complete the following statements by typing your answers in the spaces provided. If you are asked to determine the probabilities, state your answers to 4 decimal places. If you are asked to determine a value of Y, state your answers to 2 or 3 decimal places. Because you will be typing in your answers, I cannot ask you to draw diagrams as I have done in my previously posted practice finals and solutions to examples, I suggest when you are working on your answers on scrap pieces of paper (or a print out of the exam sheets), draw the diagrams. You are more likely to get the right answer if you use diagrams. For each of these statements I am asking you fill in more than one blank so that I can give you part marks if your intermediate calculation is correct but your final calculation is wrong.  

When answering each of the following, the random variable Y is normally distributed with a mean of 65 and a standard deviation of 4.

1. The value of z for being able to determine P(Y ≤ 62) is _______

The P(Y ≤ 62) is ________

2. The 2 values of z for being able to determine P( 69 ≤ Y ≤ 74) are _______ and ________

The P( 69 ≤ Y ≤ 74) is _________

3. The value of z for being able to determine P(Y ≥ 72) is _______

The P(Y ≥ 72) is ________

4. The value of z for being able to determine the value of y such that 10% of the values Y are less than that y

Is ________

               The value of y such that 10% of the values Y are less than that y is _________

Answer 1

This is a normal distribution question with

a) P(x < 62.0)=?

The z-score at x = 62.0 is,

z = -0.75

This implies that

b) P(69.0 < x < 74.0)=?

This implies that

P(69.0 < x < 74.0) = P(1.0 < z < 2.25) = P(Z < 2.25) - P(Z < 1.0)

P(69.0 < x < 74.0) = 0.9877755273449553 - 0.8413447460685429

c) P(x > 72.0)=?

The z-score at x = 72.0 is,

z = 1.75

This implies that

P(x > 72.0) = P(z > 1.75) = 1 - 0.9599408431361829

d) Given in the question

P(X < x) = 0.1

This implies that

P(Z < -1.2815515655446004) = 0.1

y = -1.28

With the help of formula for z, we can say that

Y = 59.8738

PS: you have to refer z score table to find the final probabilities.

Please hit thumps up if the answer helped you