According to an annual survey conducted by a particular website, the mean cost of a wedding in 2012 was $28,423. This is still less than the high in 2008, but it reflects increasing confidence in the economy. Suppose the cost for a wedding is normally distributed, with a standard deviation of $1,500, and a wedding is selected at random. (Round your answers to four decimal places.)(a)Find the probability that the wedding costs more than $31,000.(b)Find the probability that the wedding costs between $26,000 and $30,000.(c)Find the probability that the wedding costs less than $25,000.

(a) The probability that the wedding costs more than $31,000 is 0.0427.

(b) The probability that the wedding costs between $26,000 and $30,000 is 0.8005.

(c) The probability that the wedding costs less than $25,000 is 0.0113.

Step-by-step explanation:

Let X = cost of a wedding.

The random variable X follows a Normal distribution with mean, μ = $28, 423 and the standard deviation, σ = $1,500.

(a)

Compute the probability that the wedding costs more than $31,000 as follows:

*Use a z-table for the probability.

Thus, the probability that the wedding costs more than $31,000 is 0.0427.

(b)

Compute the probability that the wedding costs between $26,000 and $30,000 as follows:

*Use a z-table for the probability.

Thus, the probability that the wedding costs between $26,000 and $30,000 is 0.8005.

(c)

Compute the probability that the wedding costs less than $25,000 as follows:

*Use a z-table for the probability.

Thus, the probability that the wedding costs less than $25,000 is 0.0113.

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step-by-step explanation: