Question

X ~ n(-3,4). Find the probability that x is between 1 and 4.

Options:
a) 0.2119
b) 0.3085
c) 0.1056
d) 0.3944

Answer 1

To calculate the probability that x is between 1 and 4 for a normal distribution with mean -3 and variance 4, convert the x values to z-scores, find their respective CDF values, and take their difference.

Step-by-step explanation:

To find the probability that x is between 1 and 4, given that x ~ N(-3,4), you need to use the normal distribution properties. Specifically, you calculate the cumulative distribution function (CDF) for x=4 and x=1, and then subtract the CDF value at x=1 from the CDF value at x=4.

Steps to calculate the probability:

1. Convert the x values to z-scores using the formula z = (x - mean) / standard deviation.
2. Find the CDF for both z-scores using a standard normal table or a calculator function such as normcdf for TI calculators or equivalent in other tools.
3. Subtract the CDF value of the lower z-score from that of the higher z-score to find the probability that x lies between 1 and 4.