$1.30 and $1.70 is two standard deviations away from the mean on both sides of the mean, and the empirical rule for normal distribution tells us that approximately 95 percent of the data are within two standard deviations of the mean. Hence, option B is the right choice.
Data in a normal distribution is symmetrically distributed and has no skew. When displayed on a graph, the data has the shape of a bell, with most values clustering in a central region and tapering off as they go away from the center.
Because of their structure, normal distributions are sometimes known as Gaussian distributions or bell curves.
The empirical rule, often known as the 68-95-99.7 rule, indicates where the majority of your values fall in a normal distribution:
In the question, we are given that at a nearby frozen yogurt shop, the mean cost of a pint of frozen yogurt is $1.50 with a standard deviation of $0.10.
We are asked that assuming the data is normally distributed, approximately what percent of customers are willing to pay between $1.30 and $1.70 for a pint of frozen yogurt.
Following the empirical rule for a normal distribution, we need to check how many standard deviations from the mean are at $1.30 and $1.70.
$1.30 = $1.50 - 2($0.10)
and $1.70 = $1.50 + 2(0.10).
Thus, $1.30 and $1.70 is two standard deviations away from the mean on both sides of the mean, and the empirical rule for normal distribution tells us that approximately 95 percent of the data are within two standard deviations of the mean. Hence, option B is the right choice.
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