(1 point) An automobile insurer has found that repair claims are Normally distributed with a mean of $870 and a standard deviation of $810. (a) Find the probability that a single claim, chosen at random, will be less than $830.

The probability that a single claim, chosen at random, will be less than $830 is 0.48006.

Step-by-step explanation:

We are given that an automobile insurer has found that repair claims are Normally distributed with a mean of $870 and a standard deviation of $810.

Let X = repair claims

SO, X ~ N()

The z-score probability distribution is given by ;

                 Z = ~ N(0,1)

where, = mean claims = $870

            = standard deviation = $810

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, the probability that a single claim, chosen at random, will be less than $830 is given by = P(X < $830)

    P(X < $830) = P( < ) = P(Z < -0.05) = 1 - P(Z 0.05)

                                                         = 1 - 0.51994 = 0.48006

The above probability is calculated using z table by looking at value of x = 0.05 in the z table which have an area of 0.51994.

Therefore, probability that a single claim, chosen at random, will be less than $830 is 0.48006.

ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga ooga booga

step-by-step explanation:

ok

step-by-step explanation: