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In: Statistics and Probability

6.8 For normal(0,1), find a number z ∗ solving P(−z ∗ ≤ Z ≤ z ∗...

6.8 For normal(0,1), find a number z ∗ solving P(−z ∗ ≤ Z ≤ z ∗ ) = .05 (use qnorm and symmetry).R coding

6.10 Make a histogram of 100 exponential numbers with mean 10. Estimate the median. Is it more or less than the mean?

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Hey there! Thank you for the question. As you have posted 2 unrelated questions together, we have solved the first one for you.

6.8.

The “qnorm” function in R can provide the variable value for a normal variable with specified mean and standard deviation, if the cumulative probability corresponding to that value is given. The formula is to be entered in the form: qnorm(p,mean-standard_deviation), where p is the given cumulative probability.

Due to symmetry of the normal distribution,

As a result,

Now, for the standard normal variate Z, the mean is 0 and the standard deviation is 1.

Enter the following formula in an R console:

Press Enter.

The variable value is obtained as 0.0627 (correct to 4 decimal places).

Hence, the value of z* is 0.0627.

orchestra answered 1 year ago

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