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Chapter 7: Q. 7.5 (page 407)

An unknown distribution has a mean of 45 and a standard deviation of eight. A sample size of 50 is drawn randomly from the population. Find the probability that the sum of the 50 values is more than 2,400.

Short Answer

Expert verified

The probability that the sum of the 50 values is more than 2400 isP∑X>2400=0.0040.

Step by step solution

01

Given information

Given,

The value of Mean is 45.

The value of Standard deviation is8

n=50

Formula used:

∑X~N(n)μx,(n)σx
02

Find the chance that the total of the 50 values is greater than 2400.

According to the information provided, a sample size of 50 people was chosen at random from a population with a mean of 45 and a standard deviation of 8. Use a Ti-83 calculator to compute the chance that the total of 50 values is larger than 2400. To do so, go to 2nd, then DISTR, and then scroll down to the normalcdf option and fill in the required information. After that, press the calculator's ENTER key to get the desired result. The screenshot is as follows:

As a result, the likelihood of the sum of 50 values being more than 2400:

=1-0.99599=0.0040

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Most popular questions from this chapter

Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for 96days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places.

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b. Find the probability that Roberta is the driver more than 16days.

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