Question

1.- Find the following probabilities. (a) P(Z > 1.4)    (b) P(−1 < Z < 1) (c) P(Z < −1.49)

2.- Find (a) Z0.03 (b) Z0.07

3.- The distance that a Tesla model 3 can travel is normally distributed with a mean of 260 miles and a standard deviation of 25 miles.

(a) What is the probability that a randomly selected Tesla model 3 can travel more than 310 miles?

(b) What is the probability that a randomly selected Tesla model 3 can travel less than 300 miles?

(c) What is the probability that a randomly selected Tesla model 3 can travel between 235 miles and 310 miles?

(d) Now, suppose that you pick a random sample of 9 Tesla model 3. What is the probability that the sample mean will be more than 250 miles.

(e) Does the Central Limit Theorem applies in Part (d)? Explain.

Answer 1

This is a normal distribution question with

1

a) z = 1.4
This implies that
P(z > 1.4) = 0.0808

b) z1 = -1
z2 = 1
This implies that
P(-1.0 < z < 1.0) = P(z < z2) - P(z < z1)
P(-1.0 < z < 1.0) = 0.8413447460685429 - 0.8413447460685429
P(-1.0 < z < 1.0) = 0.6827

c) z = -1.49
This implies that
P(z < -1.49) = 0.0681
PS: you have to refer z score table to find the final probabilities.

2
a) z = 0.03
This implies that
P(z < 0.03) = 0.512

b) z = 0.07
This implies that
P(z < 0.07) = 0.5279
PS: you have to refer z score table to find the final probabilities.

3
This is a normal distribution question with


a) P(x > 310.0)=?
The z-score at x = 310.0 is,

This implies that


b) P(x < 300.0)=?
The z-score at x = 300.0 is,

This implies that



c) P(235.0 < x < 310.0)=?

This implies that

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

d)
Sample size (n) = 9
Since we know that

P(x > 250.0)=?
The z-score at x = 250.0 is,

This implies that

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