Question

1.Assume the random variable x is normally distributed with mean mu=83 and standard deviation sigma=5. Find the indicated probability. ​P(X<76​)

2. Find the indicated​ z-score shown in the graph to the right. Area= 0.7357

3.find the critical value tc for the confidence level c=0.99 and sample size n=7.

Answer 1

Solution :

Given that ,

1)

mean = = 83

standard deviation = = 5

P(x < 76) = P((x - ) / < (76 - 83) / 5)

= P(z < -1.4)

= 0.0808

Probability = 0.0808

2)

P(Z > z) = 0.7357

1 - P(Z < z) = 0.7357

P(Z < z) = 1 - 0.7357 = 0.2643

P(Z < -0.63) = 0.2643

z-score = -0.63

3)

sample size = n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

c = 0.99

= 1 - c = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,6 = 3.707

critical value = 3.707