Question

Assume that x has a normal distribution, and find the indicated probability.

1) The mean is 15.2 and the standard deviation is 0.9. Find the probability that x is greater than 17.

2) Let x be a continuous random variable that follows a normal distribution with a mean of 17.3 and a standard deviation of 3.2. Find the value of x so that the area under the normal curve to the left of x is .500.

Please show all the work. Thank you.

Answer 1

Solution :

Given that ,

1)

mean = = 15.2

standard deviation = = 0.9

P(x > 17) = 1 - P(x < 17)

= 1 - P((x - ) / < (17 - 15.2) / 0.9)

= 1 - P(z < 2)

= 1 - 0.9772   

= 0.0228

Probability = 0.0228

2)

P( Z < z ) = 0.500

P(Z < 0 ) = 0.500

z = 0

Using z-score formula,

X = z* +

= 0*3.2 + 17.3

= 17.3

The value of X is 17.3