Question

please help on both

1.)

We learned in section 6.1 that the Empirical Rule (a.k.a 68-95-99.7 rule) is a good estimate of probability within a specific number of standard deviations from the mean for any normal distribution.

We know that this rule only provides a good estimate and that it is not very precise. With use of the Normalcdf function in our calculator, we can find exact values. For example, when using the Empirical Rule 95% is expected to be within 2 standard deviations of the mean, when it is more precisely within  standard deviations of the mean.

Hint: To work this out, 1) sketch the distribution, 2) shade the middle 95% of the data, 3) label an unkown z-score on the horizontal axis on the upper end of the shaded portion, 4) calculate the TOTAL percentage (area) to the LEFT of the uppermost unknown z-scores, 5) finally, use invnorm to calculate the uppermost z-score. (The z-score your calator gives you in this final step is the value that you will put into the answer box above.)

2.)

Assume that the readings at freezing on a batch of thermometers are Normally distributed with mean 0°C and standard deviation 1.00°C.

Find P₉₈, the 98-percentile of the distribution of temperature readings. This is the temperature reading separating the bottom 98% from the top 2%.

°C Round to 3 decimal places.

Answer 1