the monthly electric bills in a certain community are normally distributed, with a mean of $245 and a…

the monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $35. if there are 481 households in the community, about how many of them have electric bills less than $200? table shows values to the left of the z - score\n|z|0.00|0.01|0.02|0.03|0.04|0.05|0.06|0.07|\n|----|----|----|----|----|----|----|----|----|\n|0.6|0.7257|0.7291|0.7324|0.7357|0.7389|0.7422|0.7454|0.7486|\n|0.7|0.7580|0.7611|0.7642|0.7673|0.7704|0.7734|0.7764|0.7794|\n|0.8|0.7881|0.7910|0.7939|0.7967|0.7995|0.8023|0.8051|0.8078|\n|0.9|0.8159|0.8186|0.8212|0.8238|0.8264|0.8289|0.8315|0.8340|\n|1.0|0.8413|0.8438|0.8461|0.8485|0.8508|0.8531|0.8554|0.8577|\n|1.1|0.8643|0.8665|0.8686|0.8708|0.8729|0.8749|0.8770|0.8790|\n|-1.1|0.1357|0.1335|0.1314|0.1292|0.1271|0.1251|0.1230|0.1210|\n|-1.0|0.1587|0.1562|0.1539|0.1515|0.1492|0.1469|0.1446|0.1423|\n|-0.9|0.1841|0.1814|0.1788|0.1762|0.1736|0.1711|0.1685|0.1660|\n|-0.8|0.2119|0.2090|0.2061|0.2033|0.2005|0.1977|0.1949|0.1922|\n|-0.7|0.2420|0.2389|0.2358|0.2327|0.2296|0.2266|0.2236|0.2206|\n|-0.6|0.2743|0.2709|0.2676|0.2643|0.2611|0.2578|0.2546|0.2514|\na. 21\nb. 45\nc. 81\nd. 85

the monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $35. if there are 481 households in the community, about how many of them have electric bills less than $200? table shows values to the left of the z - score\n|z|0.00|0.01|0.02|0.03|0.04|0.05|0.06|0.07|\n|----|----|----|----|----|----|----|----|----|\n|0.6|0.7257|0.7291|0.7324|0.7357|0.7389|0.7422|0.7454|0.7486|\n|0.7|0.7580|0.7611|0.7642|0.7673|0.7704|0.7734|0.7764|0.7794|\n|0.8|0.7881|0.7910|0.7939|0.7967|0.7995|0.8023|0.8051|0.8078|\n|0.9|0.8159|0.8186|0.8212|0.8238|0.8264|0.8289|0.8315|0.8340|\n|1.0|0.8413|0.8438|0.8461|0.8485|0.8508|0.8531|0.8554|0.8577|\n|1.1|0.8643|0.8665|0.8686|0.8708|0.8729|0.8749|0.8770|0.8790|\n|-1.1|0.1357|0.1335|0.1314|0.1292|0.1271|0.1251|0.1230|0.1210|\n|-1.0|0.1587|0.1562|0.1539|0.1515|0.1492|0.1469|0.1446|0.1423|\n|-0.9|0.1841|0.1814|0.1788|0.1762|0.1736|0.1711|0.1685|0.1660|\n|-0.8|0.2119|0.2090|0.2061|0.2033|0.2005|0.1977|0.1949|0.1922|\n|-0.7|0.2420|0.2389|0.2358|0.2327|0.2296|0.2266|0.2236|0.2206|\n|-0.6|0.2743|0.2709|0.2676|0.2643|0.2611|0.2578|0.2546|0.2514|\na. 21\nb. 45\nc. 81\nd. 85

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 200$, $\mu=245$, and $\sigma = 35$. $z=\frac{200 - 245}{35}=\frac{- 45}{35}\approx - 1.29$

Step2: Find the proportion from the z - table

Looking up $z=-1.29$ in the z - table (values to the left of the z - score), we find the proportion of values to the left of $z=-1.29$. Since the table doesn't have exactly $-1.29$, we take the average of the values for $z=-1.28$ and $z=-1.29$. The value for $z = - 1.28$ is $0.1003$ and for $z=-1.29$ is $0.0985$. The average is $\frac{0.1003 + 0.0985}{2}=0.0994$.

Step3: Calculate the number of households

Multiply the proportion by the total number of households. There are $n = 481$ households. The number of households with electric bills less than $200$ is $0.0994\times481\approx481\times0.1 = 48.1\approx45$ (closest value in the options)

Answer:

B. 45