Question

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 ≤ 60) is _____

The P(Y ≤ 60) is _____

2. The 2 values of z for being able to determine P( 70 ≤ Y ≤ 73) are _____ and _____

The P( 70 ≤ Y ≤ 73) is _____

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

The P(Y ≥ 72) is _____

4. The closest 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 approximate 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 < 60.0)=?

The z-score at x = 60.0 is,

z = -1.25

This implies that

b) P(70.0 < x < 73.0)=?

This implies that

P(70.0 < x < 73.0) = P(1.25 < z < 2.0) = P(Z < 2.0) - P(Z < 1.25)

P(70.0 < x < 73.0) = 0.9772498680518208 - 0.8943502263331446

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

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

x = 59.87

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

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